[{"data":1,"prerenderedAt":3837},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus":546,"formula-related-de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus":3824},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":554,"category":518,"checks":3723,"conditions":3735,"conditionsHtml":3736,"deprecated":3737,"description":3716,"extension":3738,"figure":3739,"figureCaption":3740,"figureHtml":3792,"formulaId":3793,"latex":1930,"latexHtml":3794,"level":3795,"meta":3796,"navigation":3759,"path":3797,"redirectFrom":3798,"related":3799,"seo":3804,"stem":3805,"subject":588,"summary":3806,"tags":3807,"variables":3812,"__hash__":3823},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus.md","Flächeninhalt eines Dreiecks mit Sinus",[550,551,552,553],"Dreiecksfläche mit Sinus","A = 1\u002F2 ab sin gamma","Flächeninhalt Dreieck zwei Seiten und Winkel","Dreieck Fläche ohne Höhe",{"type":555,"value":556,"toc":3715},"minimark",[557,562,575,627,1031,1366,1370,2372,2376,2534,2957,3111,3442,3446],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570,571,574],"p",{},"Mit dieser Formel berechnet man den Flächeninhalt eines ",[567,568,569],"strong",{},"beliebigen Dreiecks",", wenn zwei Seiten und der ",[567,572,573],{},"eingeschlossene Winkel"," bekannt sind. Eine Höhe muss man dafür nicht messen.",[563,576,577,578,626],{},"Wichtig ist, dass ",[579,580,583,606],"span",{"className":581},[582],"katex",[579,584,587],{"className":585},[586],"katex-mathml",[588,589,591],"math",{"xmlns":590},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[592,593,594,601],"semantics",{},[595,596,597],"mrow",{},[598,599,600],"mi",{},"γ",[602,603,605],"annotation",{"encoding":604},"application\u002Fx-tex","\\gamma",[579,607,611],{"className":608,"ariaHidden":610},[609],"katex-html","true",[579,612,615,620],{"className":613},[614],"base",[579,616],{"className":617,"style":619},[618],"strut","height:0.625em;vertical-align:-0.1944em;",[579,621,600],{"className":622,"style":625},[623,624],"mord","mathnormal","margin-right:0.0556em;"," genau der Winkel zwischen den beiden verwendeten Seiten ist. Mit anderen Seiten gilt die Formel entsprechend:",[579,628,631],{"className":629},[630],"katex-display",[579,632,634,712],{"className":633},[582],[579,635,637],{"className":636},[586],[588,638,640],{"xmlns":590,"display":639},"block",[592,641,642,709],{},[595,643,644,647,651,661,664,667,669,672,674,677,680,683,685,691,693,696,698,700,702,704,706],{},[598,645,646],{},"A",[648,649,650],"mo",{},"=",[652,653,654,658],"mfrac",{},[655,656,657],"mn",{},"1",[655,659,660],{},"2",[648,662,663],{},"⋅",[598,665,666],{},"b",[648,668,663],{},[598,670,671],{},"c",[648,673,663],{},[598,675,676],{},"sin",[648,678,679],{},"⁡",[598,681,682],{},"α",[648,684,650],{},[652,686,687,689],{},[655,688,657],{},[655,690,660],{},[648,692,663],{},[598,694,695],{},"a",[648,697,663],{},[598,699,671],{},[648,701,663],{},[598,703,676],{},[648,705,679],{},[598,707,708],{},"β",[602,710,711],{"encoding":604},"A = \\frac{1}{2} \\cdot b \\cdot c \\cdot \\sin \\alpha = \\frac{1}{2} \\cdot a \\cdot c \\cdot \\sin \\beta",[579,713,715,737,835,854,873,901,978,996,1014],{"className":714,"ariaHidden":610},[609],[579,716,718,722,725,730,734],{"className":717},[614],[579,719],{"className":720,"style":721},[618],"height:0.6833em;",[579,723,646],{"className":724},[623,624],[579,726],{"className":727,"style":729},[728],"mspace","margin-right:0.2778em;",[579,731,650],{"className":732},[733],"mrel",[579,735],{"className":736,"style":729},[728],[579,738,740,744,824,828,832],{"className":739},[614],[579,741],{"className":742,"style":743},[618],"height:2.0074em;vertical-align:-0.686em;",[579,745,747,752,820],{"className":746},[623],[579,748],{"className":749},[750,751],"mopen","nulldelimiter",[579,753,755],{"className":754},[652],[579,756,760,811],{"className":757},[758,759],"vlist-t","vlist-t2",[579,761,764,806],{"className":762},[763],"vlist-r",[579,765,769,783,794],{"className":766,"style":768},[767],"vlist","height:1.3214em;",[579,770,772,777],{"style":771},"top:-2.314em;",[579,773],{"className":774,"style":776},[775],"pstrut","height:3em;",[579,778,780],{"className":779},[623],[579,781,660],{"className":782},[623],[579,784,786,789],{"style":785},"top:-3.23em;",[579,787],{"className":788,"style":776},[775],[579,790],{"className":791,"style":793},[792],"frac-line","border-bottom-width:0.04em;",[579,795,797,800],{"style":796},"top:-3.677em;",[579,798],{"className":799,"style":776},[775],[579,801,803],{"className":802},[623],[579,804,657],{"className":805},[623],[579,807,810],{"className":808},[809],"vlist-s","​",[579,812,814],{"className":813},[763],[579,815,818],{"className":816,"style":817},[767],"height:0.686em;",[579,819],{},[579,821],{"className":822},[823,751],"mclose",[579,825],{"className":826,"style":827},[728],"margin-right:0.2222em;",[579,829,663],{"className":830},[831],"mbin",[579,833],{"className":834,"style":827},[728],[579,836,838,842,845,848,851],{"className":837},[614],[579,839],{"className":840,"style":841},[618],"height:0.6944em;",[579,843,666],{"className":844},[623,624],[579,846],{"className":847,"style":827},[728],[579,849,663],{"className":850},[831],[579,852],{"className":853,"style":827},[728],[579,855,857,861,864,867,870],{"className":856},[614],[579,858],{"className":859,"style":860},[618],"height:0.4445em;",[579,862,671],{"className":863},[623,624],[579,865],{"className":866,"style":827},[728],[579,868,663],{"className":869},[831],[579,871],{"className":872,"style":827},[728],[579,874,876,880,884,888,892,895,898],{"className":875},[614],[579,877],{"className":878,"style":879},[618],"height:0.6679em;",[579,881,676],{"className":882},[883],"mop",[579,885],{"className":886,"style":887},[728],"margin-right:0.1667em;",[579,889,682],{"className":890,"style":891},[623,624],"margin-right:0.0037em;",[579,893],{"className":894,"style":729},[728],[579,896,650],{"className":897},[733],[579,899],{"className":900,"style":729},[728],[579,902,904,907,969,972,975],{"className":903},[614],[579,905],{"className":906,"style":743},[618],[579,908,910,913,966],{"className":909},[623],[579,911],{"className":912},[750,751],[579,914,916],{"className":915},[652],[579,917,919,958],{"className":918},[758,759],[579,920,922,955],{"className":921},[763],[579,923,925,936,944],{"className":924,"style":768},[767],[579,926,927,930],{"style":771},[579,928],{"className":929,"style":776},[775],[579,931,933],{"className":932},[623],[579,934,660],{"className":935},[623],[579,937,938,941],{"style":785},[579,939],{"className":940,"style":776},[775],[579,942],{"className":943,"style":793},[792],[579,945,946,949],{"style":796},[579,947],{"className":948,"style":776},[775],[579,950,952],{"className":951},[623],[579,953,657],{"className":954},[623],[579,956,810],{"className":957},[809],[579,959,961],{"className":960},[763],[579,962,964],{"className":963,"style":817},[767],[579,965],{},[579,967],{"className":968},[823,751],[579,970],{"className":971,"style":827},[728],[579,973,663],{"className":974},[831],[579,976],{"className":977,"style":827},[728],[579,979,981,984,987,990,993],{"className":980},[614],[579,982],{"className":983,"style":860},[618],[579,985,695],{"className":986},[623,624],[579,988],{"className":989,"style":827},[728],[579,991,663],{"className":992},[831],[579,994],{"className":995,"style":827},[728],[579,997,999,1002,1005,1008,1011],{"className":998},[614],[579,1000],{"className":1001,"style":860},[618],[579,1003,671],{"className":1004},[623,624],[579,1006],{"className":1007,"style":827},[728],[579,1009,663],{"className":1010},[831],[579,1012],{"className":1013,"style":827},[728],[579,1015,1017,1021,1024,1027],{"className":1016},[614],[579,1018],{"className":1019,"style":1020},[618],"height:0.8889em;vertical-align:-0.1944em;",[579,1022,676],{"className":1023},[883],[579,1025],{"className":1026,"style":887},[728],[579,1028,708],{"className":1029,"style":1030},[623,624],"margin-right:0.0528em;",[563,1032,1033,1034,1131,1132,1195,1196,1365],{},"Bei ",[579,1035,1037,1062],{"className":1036},[582],[579,1038,1040],{"className":1039},[586],[588,1041,1042],{"xmlns":590},[592,1043,1044,1059],{},[595,1045,1046,1048,1050],{},[598,1047,600],{},[648,1049,650],{},[1051,1052,1053,1056],"msup",{},[655,1054,1055],{},"90",[648,1057,1058],{},"∘",[602,1060,1061],{"encoding":604},"\\gamma = 90^\\circ",[579,1063,1065,1083],{"className":1064,"ariaHidden":610},[609],[579,1066,1068,1071,1074,1077,1080],{"className":1067},[614],[579,1069],{"className":1070,"style":619},[618],[579,1072,600],{"className":1073,"style":625},[623,624],[579,1075],{"className":1076,"style":729},[728],[579,1078,650],{"className":1079},[733],[579,1081],{"className":1082,"style":729},[728],[579,1084,1086,1090,1094],{"className":1085},[614],[579,1087],{"className":1088,"style":1089},[618],"height:0.6741em;",[579,1091,1093],{"className":1092},[623],"9",[579,1095,1097,1101],{"className":1096},[623],[579,1098,1100],{"className":1099},[623],"0",[579,1102,1105],{"className":1103},[1104],"msupsub",[579,1106,1108],{"className":1107},[758],[579,1109,1111],{"className":1110},[763],[579,1112,1114],{"className":1113,"style":1089},[767],[579,1115,1117,1121],{"style":1116},"top:-3.063em;margin-right:0.05em;",[579,1118],{"className":1119,"style":1120},[775],"height:2.7em;",[579,1122,1128],{"className":1123},[1124,1125,1126,1127],"sizing","reset-size6","size3","mtight",[579,1129,1058],{"className":1130},[831,1127]," ist ",[579,1133,1135,1157],{"className":1134},[582],[579,1136,1138],{"className":1137},[586],[588,1139,1140],{"xmlns":590},[592,1141,1142,1154],{},[595,1143,1144,1146,1148,1150,1152],{},[598,1145,676],{},[648,1147,679],{},[598,1149,600],{},[648,1151,650],{},[655,1153,657],{},[602,1155,1156],{"encoding":604},"\\sin \\gamma = 1",[579,1158,1160,1185],{"className":1159,"ariaHidden":610},[609],[579,1161,1163,1167,1170,1173,1176,1179,1182],{"className":1162},[614],[579,1164],{"className":1165,"style":1166},[618],"height:0.8623em;vertical-align:-0.1944em;",[579,1168,676],{"className":1169},[883],[579,1171],{"className":1172,"style":887},[728],[579,1174,600],{"className":1175,"style":625},[623,624],[579,1177],{"className":1178,"style":729},[728],[579,1180,650],{"className":1181},[733],[579,1183],{"className":1184,"style":729},[728],[579,1186,1188,1192],{"className":1187},[614],[579,1189],{"className":1190,"style":1191},[618],"height:0.6444em;",[579,1193,657],{"className":1194},[623],", und es bleibt ",[579,1197,1199,1229],{"className":1198},[582],[579,1200,1202],{"className":1201},[586],[588,1203,1204],{"xmlns":590},[592,1205,1206,1226],{},[595,1207,1208,1210,1212,1218,1220,1222,1224],{},[598,1209,646],{},[648,1211,650],{},[652,1213,1214,1216],{},[655,1215,657],{},[655,1217,660],{},[648,1219,663],{},[598,1221,695],{},[648,1223,663],{},[598,1225,666],{},[602,1227,1228],{"encoding":604},"A = \\frac{1}{2} \\cdot a \\cdot b",[579,1230,1232,1250,1338,1356],{"className":1231,"ariaHidden":610},[609],[579,1233,1235,1238,1241,1244,1247],{"className":1234},[614],[579,1236],{"className":1237,"style":721},[618],[579,1239,646],{"className":1240},[623,624],[579,1242],{"className":1243,"style":729},[728],[579,1245,650],{"className":1246},[733],[579,1248],{"className":1249,"style":729},[728],[579,1251,1253,1257,1329,1332,1335],{"className":1252},[614],[579,1254],{"className":1255,"style":1256},[618],"height:1.1901em;vertical-align:-0.345em;",[579,1258,1260,1263,1326],{"className":1259},[623],[579,1261],{"className":1262},[750,751],[579,1264,1266],{"className":1265},[652],[579,1267,1269,1317],{"className":1268},[758,759],[579,1270,1272,1314],{"className":1271},[763],[579,1273,1276,1291,1299],{"className":1274,"style":1275},[767],"height:0.8451em;",[579,1277,1279,1282],{"style":1278},"top:-2.655em;",[579,1280],{"className":1281,"style":776},[775],[579,1283,1285],{"className":1284},[1124,1125,1126,1127],[579,1286,1288],{"className":1287},[623,1127],[579,1289,660],{"className":1290},[623,1127],[579,1292,1293,1296],{"style":785},[579,1294],{"className":1295,"style":776},[775],[579,1297],{"className":1298,"style":793},[792],[579,1300,1302,1305],{"style":1301},"top:-3.394em;",[579,1303],{"className":1304,"style":776},[775],[579,1306,1308],{"className":1307},[1124,1125,1126,1127],[579,1309,1311],{"className":1310},[623,1127],[579,1312,657],{"className":1313},[623,1127],[579,1315,810],{"className":1316},[809],[579,1318,1320],{"className":1319},[763],[579,1321,1324],{"className":1322,"style":1323},[767],"height:0.345em;",[579,1325],{},[579,1327],{"className":1328},[823,751],[579,1330],{"className":1331,"style":827},[728],[579,1333,663],{"className":1334},[831],[579,1336],{"className":1337,"style":827},[728],[579,1339,1341,1344,1347,1350,1353],{"className":1340},[614],[579,1342],{"className":1343,"style":860},[618],[579,1345,695],{"className":1346},[623,624],[579,1348],{"className":1349,"style":827},[728],[579,1351,663],{"className":1352},[831],[579,1354],{"className":1355,"style":827},[728],[579,1357,1359,1362],{"className":1358},[614],[579,1360],{"className":1361,"style":841},[618],[579,1363,666],{"className":1364},[623,624],", die bekannte Formel für das rechtwinklige Dreieck.",[558,1367,1369],{"id":1368},"herleitung","Herleitung",[563,1371,1372,1373,1599,1600,1629,1630,1706,1707,1735,1736,1764,1765,1889,1890,2086,2087,2115,2116,2144,2145,2233,2234,2371],{},"Die übliche Flächenformel lautet ",[579,1374,1376,1423],{"className":1375},[582],[579,1377,1379],{"className":1378},[586],[588,1380,1381],{"xmlns":590},[592,1382,1383,1420],{},[595,1384,1385,1387,1389,1395,1397,1401,1403],{},[598,1386,646],{},[648,1388,650],{},[652,1390,1391,1393],{},[655,1392,657],{},[655,1394,660],{},[648,1396,663],{},[1398,1399,1400],"mtext",{},"Grundseite",[648,1402,663],{},[595,1404,1405,1408,1417],{},[1398,1406,1407],{},"H",[1409,1410,1411,1414],"mover",{"accent":610},[1398,1412,1413],{},"o",[648,1415,1416],{},"¨",[1398,1418,1419],{},"he",[602,1421,1422],{"encoding":604},"A = \\frac{1}{2} \\cdot \\text{Grundseite} \\cdot \\text{Höhe}",[579,1424,1426,1444,1527,1549],{"className":1425,"ariaHidden":610},[609],[579,1427,1429,1432,1435,1438,1441],{"className":1428},[614],[579,1430],{"className":1431,"style":721},[618],[579,1433,646],{"className":1434},[623,624],[579,1436],{"className":1437,"style":729},[728],[579,1439,650],{"className":1440},[733],[579,1442],{"className":1443,"style":729},[728],[579,1445,1447,1450,1518,1521,1524],{"className":1446},[614],[579,1448],{"className":1449,"style":1256},[618],[579,1451,1453,1456,1515],{"className":1452},[623],[579,1454],{"className":1455},[750,751],[579,1457,1459],{"className":1458},[652],[579,1460,1462,1507],{"className":1461},[758,759],[579,1463,1465,1504],{"className":1464},[763],[579,1466,1468,1482,1490],{"className":1467,"style":1275},[767],[579,1469,1470,1473],{"style":1278},[579,1471],{"className":1472,"style":776},[775],[579,1474,1476],{"className":1475},[1124,1125,1126,1127],[579,1477,1479],{"className":1478},[623,1127],[579,1480,660],{"className":1481},[623,1127],[579,1483,1484,1487],{"style":785},[579,1485],{"className":1486,"style":776},[775],[579,1488],{"className":1489,"style":793},[792],[579,1491,1492,1495],{"style":1301},[579,1493],{"className":1494,"style":776},[775],[579,1496,1498],{"className":1497},[1124,1125,1126,1127],[579,1499,1501],{"className":1500},[623,1127],[579,1502,657],{"className":1503},[623,1127],[579,1505,810],{"className":1506},[809],[579,1508,1510],{"className":1509},[763],[579,1511,1513],{"className":1512,"style":1323},[767],[579,1514],{},[579,1516],{"className":1517},[823,751],[579,1519],{"className":1520,"style":827},[728],[579,1522,663],{"className":1523},[831],[579,1525],{"className":1526,"style":827},[728],[579,1528,1530,1533,1540,1543,1546],{"className":1529},[614],[579,1531],{"className":1532,"style":841},[618],[579,1534,1537],{"className":1535},[623,1536],"text",[579,1538,1400],{"className":1539},[623],[579,1541],{"className":1542,"style":827},[728],[579,1544,663],{"className":1545},[831],[579,1547],{"className":1548,"style":827},[728],[579,1550,1552,1555],{"className":1551},[614],[579,1553],{"className":1554,"style":841},[618],[579,1556,1558,1561,1596],{"className":1557},[623,1536],[579,1559,1407],{"className":1560},[623],[579,1562,1565],{"className":1563},[623,1564],"accent",[579,1566,1568],{"className":1567},[758],[579,1569,1571],{"className":1570},[763],[579,1572,1574,1583],{"className":1573,"style":879},[767],[579,1575,1577,1580],{"style":1576},"top:-3em;",[579,1578],{"className":1579,"style":776},[775],[579,1581,1413],{"className":1582},[623],[579,1584,1585,1588],{"style":1576},[579,1586],{"className":1587,"style":776},[775],[579,1589,1593],{"className":1590,"style":1592},[1591],"accent-body","left:-0.25em;",[579,1594,1416],{"className":1595},[623],[579,1597,1419],{"className":1598},[623],". Nimmt man ",[579,1601,1603,1616],{"className":1602},[582],[579,1604,1606],{"className":1605},[586],[588,1607,1608],{"xmlns":590},[592,1609,1610,1614],{},[595,1611,1612],{},[598,1613,695],{},[602,1615,695],{"encoding":604},[579,1617,1619],{"className":1618,"ariaHidden":610},[609],[579,1620,1622,1626],{"className":1621},[614],[579,1623],{"className":1624,"style":1625},[618],"height:0.4306em;",[579,1627,695],{"className":1628},[623,624]," als Grundseite, ist die Höhe ",[579,1631,1633,1653],{"className":1632},[582],[579,1634,1636],{"className":1635},[586],[588,1637,1638],{"xmlns":590},[592,1639,1640,1650],{},[595,1641,1642],{},[1643,1644,1645,1648],"msub",{},[598,1646,1647],{},"h",[598,1649,695],{},[602,1651,1652],{"encoding":604},"h_a",[579,1654,1656],{"className":1655,"ariaHidden":610},[609],[579,1657,1659,1663],{"className":1658},[614],[579,1660],{"className":1661,"style":1662},[618],"height:0.8444em;vertical-align:-0.15em;",[579,1664,1666,1669],{"className":1665},[623],[579,1667,1647],{"className":1668},[623,624],[579,1670,1672],{"className":1671},[1104],[579,1673,1675,1697],{"className":1674},[758,759],[579,1676,1678,1694],{"className":1677},[763],[579,1679,1682],{"className":1680,"style":1681},[767],"height:0.1514em;",[579,1683,1685,1688],{"style":1684},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[579,1686],{"className":1687,"style":1120},[775],[579,1689,1691],{"className":1690},[1124,1125,1126,1127],[579,1692,695],{"className":1693},[623,624,1127],[579,1695,810],{"className":1696},[809],[579,1698,1700],{"className":1699},[763],[579,1701,1704],{"className":1702,"style":1703},[767],"height:0.15em;",[579,1705],{}," die Gegenkathete von ",[579,1708,1710,1723],{"className":1709},[582],[579,1711,1713],{"className":1712},[586],[588,1714,1715],{"xmlns":590},[592,1716,1717,1721],{},[595,1718,1719],{},[598,1720,600],{},[602,1722,605],{"encoding":604},[579,1724,1726],{"className":1725,"ariaHidden":610},[609],[579,1727,1729,1732],{"className":1728},[614],[579,1730],{"className":1731,"style":619},[618],[579,1733,600],{"className":1734,"style":625},[623,624]," in einem rechtwinkligen Teildreieck mit der Hypotenuse ",[579,1737,1739,1752],{"className":1738},[582],[579,1740,1742],{"className":1741},[586],[588,1743,1744],{"xmlns":590},[592,1745,1746,1750],{},[595,1747,1748],{},[598,1749,666],{},[602,1751,666],{"encoding":604},[579,1753,1755],{"className":1754,"ariaHidden":610},[609],[579,1756,1758,1761],{"className":1757},[614],[579,1759],{"className":1760,"style":841},[618],[579,1762,666],{"className":1763},[623,624],". Also ist ",[579,1766,1768,1798],{"className":1767},[582],[579,1769,1771],{"className":1770},[586],[588,1772,1773],{"xmlns":590},[592,1774,1775,1795],{},[595,1776,1777,1783,1785,1787,1789,1791,1793],{},[1643,1778,1779,1781],{},[598,1780,1647],{},[598,1782,695],{},[648,1784,650],{},[598,1786,666],{},[648,1788,663],{},[598,1790,676],{},[648,1792,679],{},[598,1794,600],{},[602,1796,1797],{"encoding":604},"h_a = b \\cdot \\sin \\gamma",[579,1799,1801,1856,1874],{"className":1800,"ariaHidden":610},[609],[579,1802,1804,1807,1847,1850,1853],{"className":1803},[614],[579,1805],{"className":1806,"style":1662},[618],[579,1808,1810,1813],{"className":1809},[623],[579,1811,1647],{"className":1812},[623,624],[579,1814,1816],{"className":1815},[1104],[579,1817,1819,1839],{"className":1818},[758,759],[579,1820,1822,1836],{"className":1821},[763],[579,1823,1825],{"className":1824,"style":1681},[767],[579,1826,1827,1830],{"style":1684},[579,1828],{"className":1829,"style":1120},[775],[579,1831,1833],{"className":1832},[1124,1125,1126,1127],[579,1834,695],{"className":1835},[623,624,1127],[579,1837,810],{"className":1838},[809],[579,1840,1842],{"className":1841},[763],[579,1843,1845],{"className":1844,"style":1703},[767],[579,1846],{},[579,1848],{"className":1849,"style":729},[728],[579,1851,650],{"className":1852},[733],[579,1854],{"className":1855,"style":729},[728],[579,1857,1859,1862,1865,1868,1871],{"className":1858},[614],[579,1860],{"className":1861,"style":841},[618],[579,1863,666],{"className":1864},[623,624],[579,1866],{"className":1867,"style":827},[728],[579,1869,663],{"className":1870},[831],[579,1872],{"className":1873,"style":827},[728],[579,1875,1877,1880,1883,1886],{"className":1876},[614],[579,1878],{"className":1879,"style":1166},[618],[579,1881,676],{"className":1882},[883],[579,1884],{"className":1885,"style":887},[728],[579,1887,600],{"className":1888,"style":625},[623,624]," und damit ",[579,1891,1893,1931],{"className":1892},[582],[579,1894,1896],{"className":1895},[586],[588,1897,1898],{"xmlns":590},[592,1899,1900,1928],{},[595,1901,1902,1904,1906,1912,1914,1916,1918,1920,1922,1924,1926],{},[598,1903,646],{},[648,1905,650],{},[652,1907,1908,1910],{},[655,1909,657],{},[655,1911,660],{},[648,1913,663],{},[598,1915,695],{},[648,1917,663],{},[598,1919,666],{},[648,1921,663],{},[598,1923,676],{},[648,1925,679],{},[598,1927,600],{},[602,1929,1930],{"encoding":604},"A = \\frac{1}{2} \\cdot a \\cdot b \\cdot \\sin \\gamma",[579,1932,1934,1952,2035,2053,2071],{"className":1933,"ariaHidden":610},[609],[579,1935,1937,1940,1943,1946,1949],{"className":1936},[614],[579,1938],{"className":1939,"style":721},[618],[579,1941,646],{"className":1942},[623,624],[579,1944],{"className":1945,"style":729},[728],[579,1947,650],{"className":1948},[733],[579,1950],{"className":1951,"style":729},[728],[579,1953,1955,1958,2026,2029,2032],{"className":1954},[614],[579,1956],{"className":1957,"style":1256},[618],[579,1959,1961,1964,2023],{"className":1960},[623],[579,1962],{"className":1963},[750,751],[579,1965,1967],{"className":1966},[652],[579,1968,1970,2015],{"className":1969},[758,759],[579,1971,1973,2012],{"className":1972},[763],[579,1974,1976,1990,1998],{"className":1975,"style":1275},[767],[579,1977,1978,1981],{"style":1278},[579,1979],{"className":1980,"style":776},[775],[579,1982,1984],{"className":1983},[1124,1125,1126,1127],[579,1985,1987],{"className":1986},[623,1127],[579,1988,660],{"className":1989},[623,1127],[579,1991,1992,1995],{"style":785},[579,1993],{"className":1994,"style":776},[775],[579,1996],{"className":1997,"style":793},[792],[579,1999,2000,2003],{"style":1301},[579,2001],{"className":2002,"style":776},[775],[579,2004,2006],{"className":2005},[1124,1125,1126,1127],[579,2007,2009],{"className":2008},[623,1127],[579,2010,657],{"className":2011},[623,1127],[579,2013,810],{"className":2014},[809],[579,2016,2018],{"className":2017},[763],[579,2019,2021],{"className":2020,"style":1323},[767],[579,2022],{},[579,2024],{"className":2025},[823,751],[579,2027],{"className":2028,"style":827},[728],[579,2030,663],{"className":2031},[831],[579,2033],{"className":2034,"style":827},[728],[579,2036,2038,2041,2044,2047,2050],{"className":2037},[614],[579,2039],{"className":2040,"style":860},[618],[579,2042,695],{"className":2043},[623,624],[579,2045],{"className":2046,"style":827},[728],[579,2048,663],{"className":2049},[831],[579,2051],{"className":2052,"style":827},[728],[579,2054,2056,2059,2062,2065,2068],{"className":2055},[614],[579,2057],{"className":2058,"style":841},[618],[579,2060,666],{"className":2061},[623,624],[579,2063],{"className":2064,"style":827},[728],[579,2066,663],{"className":2067},[831],[579,2069],{"className":2070,"style":827},[728],[579,2072,2074,2077,2080,2083],{"className":2073},[614],[579,2075],{"className":2076,"style":1166},[618],[579,2078,676],{"className":2079},[883],[579,2081],{"className":2082,"style":887},[728],[579,2084,600],{"className":2085,"style":625},[623,624],". Ist ",[579,2088,2090,2103],{"className":2089},[582],[579,2091,2093],{"className":2092},[586],[588,2094,2095],{"xmlns":590},[592,2096,2097,2101],{},[595,2098,2099],{},[598,2100,600],{},[602,2102,605],{"encoding":604},[579,2104,2106],{"className":2105,"ariaHidden":610},[609],[579,2107,2109,2112],{"className":2108},[614],[579,2110],{"className":2111,"style":619},[618],[579,2113,600],{"className":2114,"style":625},[623,624]," stumpf, liegt der Fußpunkt der Höhe außerhalb des Dreiecks, auf der Verlängerung von ",[579,2117,2119,2132],{"className":2118},[582],[579,2120,2122],{"className":2121},[586],[588,2123,2124],{"xmlns":590},[592,2125,2126,2130],{},[595,2127,2128],{},[598,2129,695],{},[602,2131,695],{"encoding":604},[579,2133,2135],{"className":2134,"ariaHidden":610},[609],[579,2136,2138,2141],{"className":2137},[614],[579,2139],{"className":2140,"style":1625},[618],[579,2142,695],{"className":2143},[623,624],". Im Teildreieck steht dann der Winkel ",[579,2146,2148,2172],{"className":2147},[582],[579,2149,2151],{"className":2150},[586],[588,2152,2153],{"xmlns":590},[592,2154,2155,2169],{},[595,2156,2157,2164,2167],{},[1051,2158,2159,2162],{},[655,2160,2161],{},"180",[648,2163,1058],{},[648,2165,2166],{},"−",[598,2168,600],{},[602,2170,2171],{"encoding":604},"180^\\circ - \\gamma",[579,2173,2175,2224],{"className":2174,"ariaHidden":610},[609],[579,2176,2178,2182,2186,2215,2218,2221],{"className":2177},[614],[579,2179],{"className":2180,"style":2181},[618],"height:0.7574em;vertical-align:-0.0833em;",[579,2183,2185],{"className":2184},[623],"18",[579,2187,2189,2192],{"className":2188},[623],[579,2190,1100],{"className":2191},[623],[579,2193,2195],{"className":2194},[1104],[579,2196,2198],{"className":2197},[758],[579,2199,2201],{"className":2200},[763],[579,2202,2204],{"className":2203,"style":1089},[767],[579,2205,2206,2209],{"style":1116},[579,2207],{"className":2208,"style":1120},[775],[579,2210,2212],{"className":2211},[1124,1125,1126,1127],[579,2213,1058],{"className":2214},[831,1127],[579,2216],{"className":2217,"style":827},[728],[579,2219,2166],{"className":2220},[831],[579,2222],{"className":2223,"style":827},[728],[579,2225,2227,2230],{"className":2226},[614],[579,2228],{"className":2229,"style":619},[618],[579,2231,600],{"className":2232,"style":625},[623,624],", und wegen ",[579,2235,2237,2278],{"className":2236},[582],[579,2238,2240],{"className":2239},[586],[588,2241,2242],{"xmlns":590},[592,2243,2244,2275],{},[595,2245,2246,2248,2250,2254,2260,2262,2264,2267,2269,2271,2273],{},[598,2247,676],{},[648,2249,679],{},[648,2251,2253],{"stretchy":2252},"false","(",[1051,2255,2256,2258],{},[655,2257,2161],{},[648,2259,1058],{},[648,2261,2166],{},[598,2263,600],{},[648,2265,2266],{"stretchy":2252},")",[648,2268,650],{},[598,2270,676],{},[648,2272,679],{},[598,2274,600],{},[602,2276,2277],{"encoding":604},"\\sin(180^\\circ - \\gamma) = \\sin \\gamma",[579,2279,2281,2335,2356],{"className":2280,"ariaHidden":610},[609],[579,2282,2284,2288,2291,2294,2297,2326,2329,2332],{"className":2283},[614],[579,2285],{"className":2286,"style":2287},[618],"height:1em;vertical-align:-0.25em;",[579,2289,676],{"className":2290},[883],[579,2292,2253],{"className":2293},[750],[579,2295,2185],{"className":2296},[623],[579,2298,2300,2303],{"className":2299},[623],[579,2301,1100],{"className":2302},[623],[579,2304,2306],{"className":2305},[1104],[579,2307,2309],{"className":2308},[758],[579,2310,2312],{"className":2311},[763],[579,2313,2315],{"className":2314,"style":1089},[767],[579,2316,2317,2320],{"style":1116},[579,2318],{"className":2319,"style":1120},[775],[579,2321,2323],{"className":2322},[1124,1125,1126,1127],[579,2324,1058],{"className":2325},[831,1127],[579,2327],{"className":2328,"style":827},[728],[579,2330,2166],{"className":2331},[831],[579,2333],{"className":2334,"style":827},[728],[579,2336,2338,2341,2344,2347,2350,2353],{"className":2337},[614],[579,2339],{"className":2340,"style":2287},[618],[579,2342,600],{"className":2343,"style":625},[623,624],[579,2345,2266],{"className":2346},[823],[579,2348],{"className":2349,"style":729},[728],[579,2351,650],{"className":2352},[733],[579,2354],{"className":2355,"style":729},[728],[579,2357,2359,2362,2365,2368],{"className":2358},[614],[579,2360],{"className":2361,"style":1166},[618],[579,2363,676],{"className":2364},[883],[579,2366],{"className":2367,"style":887},[728],[579,2369,600],{"className":2370,"style":625},[623,624]," gilt die Formel weiterhin.",[558,2373,2375],{"id":2374},"beispiele","Beispiele",[563,2377,2378,2379,2424,2425,2468,2469,2533],{},"Zwei Seiten sind ",[579,2380,2382,2403],{"className":2381},[582],[579,2383,2385],{"className":2384},[586],[588,2386,2387],{"xmlns":590},[592,2388,2389,2400],{},[595,2390,2391,2394,2397],{},[655,2392,2393],{},"6",[1398,2395,2396],{}," ",[1398,2398,2399],{},"cm",[602,2401,2402],{"encoding":604},"6\\,\\text{cm}",[579,2404,2406],{"className":2405,"ariaHidden":610},[609],[579,2407,2409,2412,2415,2418],{"className":2408},[614],[579,2410],{"className":2411,"style":1191},[618],[579,2413,2393],{"className":2414},[623],[579,2416],{"className":2417,"style":887},[728],[579,2419,2421],{"className":2420},[623,1536],[579,2422,2399],{"className":2423},[623]," und ",[579,2426,2428,2447],{"className":2427},[582],[579,2429,2431],{"className":2430},[586],[588,2432,2433],{"xmlns":590},[592,2434,2435,2444],{},[595,2436,2437,2440,2442],{},[655,2438,2439],{},"8",[1398,2441,2396],{},[1398,2443,2399],{},[602,2445,2446],{"encoding":604},"8\\,\\text{cm}",[579,2448,2450],{"className":2449,"ariaHidden":610},[609],[579,2451,2453,2456,2459,2462],{"className":2452},[614],[579,2454],{"className":2455,"style":1191},[618],[579,2457,2439],{"className":2458},[623],[579,2460],{"className":2461,"style":887},[728],[579,2463,2465],{"className":2464},[623,1536],[579,2466,2399],{"className":2467},[623]," lang und schließen einen Winkel von ",[579,2470,2472,2491],{"className":2471},[582],[579,2473,2475],{"className":2474},[586],[588,2476,2477],{"xmlns":590},[592,2478,2479,2488],{},[595,2480,2481],{},[1051,2482,2483,2486],{},[655,2484,2485],{},"30",[648,2487,1058],{},[602,2489,2490],{"encoding":604},"30^\\circ",[579,2492,2494],{"className":2493,"ariaHidden":610},[609],[579,2495,2497,2500,2504],{"className":2496},[614],[579,2498],{"className":2499,"style":1089},[618],[579,2501,2503],{"className":2502},[623],"3",[579,2505,2507,2510],{"className":2506},[623],[579,2508,1100],{"className":2509},[623],[579,2511,2513],{"className":2512},[1104],[579,2514,2516],{"className":2515},[758],[579,2517,2519],{"className":2518},[763],[579,2520,2522],{"className":2521,"style":1089},[767],[579,2523,2524,2527],{"style":1116},[579,2525],{"className":2526,"style":1120},[775],[579,2528,2530],{"className":2529},[1124,1125,1126,1127],[579,2531,1058],{"className":2532},[831,1127]," ein:",[579,2535,2537],{"className":2536},[630],[579,2538,2540,2621],{"className":2539},[582],[579,2541,2543],{"className":2542},[586],[588,2544,2545],{"xmlns":590,"display":639},[592,2546,2547,2618],{},[595,2548,2549,2551,2553,2559,2561,2563,2565,2567,2569,2571,2573,2575,2577,2579,2581,2587,2589,2592,2594,2600,2602,2605,2607,2610,2612],{},[598,2550,646],{},[648,2552,650],{},[652,2554,2555,2557],{},[655,2556,657],{},[655,2558,660],{},[648,2560,663],{},[655,2562,2393],{},[1398,2564,2396],{},[1398,2566,2399],{},[648,2568,663],{},[655,2570,2439],{},[1398,2572,2396],{},[1398,2574,2399],{},[648,2576,663],{},[598,2578,676],{},[648,2580,679],{},[1051,2582,2583,2585],{},[655,2584,2485],{},[648,2586,1058],{},[648,2588,650],{},[655,2590,2591],{},"24",[1398,2593,2396],{},[1051,2595,2596,2598],{},[1398,2597,2399],{},[655,2599,660],{},[648,2601,663],{},[655,2603,2604],{},"0,5",[648,2606,650],{},[655,2608,2609],{},"12",[1398,2611,2396],{},[1051,2613,2614,2616],{},[1398,2615,2399],{},[655,2617,660],{},[602,2619,2620],{"encoding":604},"A = \\frac{1}{2} \\cdot 6\\,\\text{cm} \\cdot 8\\,\\text{cm} \\cdot \\sin 30^\\circ = 24\\,\\text{cm}^2 \\cdot 0{,}5 = 12\\,\\text{cm}^2",[579,2622,2624,2642,2719,2746,2773,2828,2882,2913],{"className":2623,"ariaHidden":610},[609],[579,2625,2627,2630,2633,2636,2639],{"className":2626},[614],[579,2628],{"className":2629,"style":721},[618],[579,2631,646],{"className":2632},[623,624],[579,2634],{"className":2635,"style":729},[728],[579,2637,650],{"className":2638},[733],[579,2640],{"className":2641,"style":729},[728],[579,2643,2645,2648,2710,2713,2716],{"className":2644},[614],[579,2646],{"className":2647,"style":743},[618],[579,2649,2651,2654,2707],{"className":2650},[623],[579,2652],{"className":2653},[750,751],[579,2655,2657],{"className":2656},[652],[579,2658,2660,2699],{"className":2659},[758,759],[579,2661,2663,2696],{"className":2662},[763],[579,2664,2666,2677,2685],{"className":2665,"style":768},[767],[579,2667,2668,2671],{"style":771},[579,2669],{"className":2670,"style":776},[775],[579,2672,2674],{"className":2673},[623],[579,2675,660],{"className":2676},[623],[579,2678,2679,2682],{"style":785},[579,2680],{"className":2681,"style":776},[775],[579,2683],{"className":2684,"style":793},[792],[579,2686,2687,2690],{"style":796},[579,2688],{"className":2689,"style":776},[775],[579,2691,2693],{"className":2692},[623],[579,2694,657],{"className":2695},[623],[579,2697,810],{"className":2698},[809],[579,2700,2702],{"className":2701},[763],[579,2703,2705],{"className":2704,"style":817},[767],[579,2706],{},[579,2708],{"className":2709},[823,751],[579,2711],{"className":2712,"style":827},[728],[579,2714,663],{"className":2715},[831],[579,2717],{"className":2718,"style":827},[728],[579,2720,2722,2725,2728,2731,2737,2740,2743],{"className":2721},[614],[579,2723],{"className":2724,"style":1191},[618],[579,2726,2393],{"className":2727},[623],[579,2729],{"className":2730,"style":887},[728],[579,2732,2734],{"className":2733},[623,1536],[579,2735,2399],{"className":2736},[623],[579,2738],{"className":2739,"style":827},[728],[579,2741,663],{"className":2742},[831],[579,2744],{"className":2745,"style":827},[728],[579,2747,2749,2752,2755,2758,2764,2767,2770],{"className":2748},[614],[579,2750],{"className":2751,"style":1191},[618],[579,2753,2439],{"className":2754},[623],[579,2756],{"className":2757,"style":887},[728],[579,2759,2761],{"className":2760},[623,1536],[579,2762,2399],{"className":2763},[623],[579,2765],{"className":2766,"style":827},[728],[579,2768,663],{"className":2769},[831],[579,2771],{"className":2772,"style":827},[728],[579,2774,2776,2780,2783,2786,2789,2819,2822,2825],{"className":2775},[614],[579,2777],{"className":2778,"style":2779},[618],"height:0.7241em;",[579,2781,676],{"className":2782},[883],[579,2784],{"className":2785,"style":887},[728],[579,2787,2503],{"className":2788},[623],[579,2790,2792,2795],{"className":2791},[623],[579,2793,1100],{"className":2794},[623],[579,2796,2798],{"className":2797},[1104],[579,2799,2801],{"className":2800},[758],[579,2802,2804],{"className":2803},[763],[579,2805,2807],{"className":2806,"style":2779},[767],[579,2808,2810,2813],{"style":2809},"top:-3.113em;margin-right:0.05em;",[579,2811],{"className":2812,"style":1120},[775],[579,2814,2816],{"className":2815},[1124,1125,1126,1127],[579,2817,1058],{"className":2818},[831,1127],[579,2820],{"className":2821,"style":729},[728],[579,2823,650],{"className":2824},[733],[579,2826],{"className":2827,"style":729},[728],[579,2829,2831,2835,2838,2841,2873,2876,2879],{"className":2830},[614],[579,2832],{"className":2833,"style":2834},[618],"height:0.8641em;",[579,2836,2591],{"className":2837},[623],[579,2839],{"className":2840,"style":887},[728],[579,2842,2844,2850],{"className":2843},[623],[579,2845,2847],{"className":2846},[623,1536],[579,2848,2399],{"className":2849},[623],[579,2851,2853],{"className":2852},[1104],[579,2854,2856],{"className":2855},[758],[579,2857,2859],{"className":2858},[763],[579,2860,2862],{"className":2861,"style":2834},[767],[579,2863,2864,2867],{"style":2809},[579,2865],{"className":2866,"style":1120},[775],[579,2868,2870],{"className":2869},[1124,1125,1126,1127],[579,2871,660],{"className":2872},[623,1127],[579,2874],{"className":2875,"style":827},[728],[579,2877,663],{"className":2878},[831],[579,2880],{"className":2881,"style":827},[728],[579,2883,2885,2889,2892,2900,2904,2907,2910],{"className":2884},[614],[579,2886],{"className":2887,"style":2888},[618],"height:0.8389em;vertical-align:-0.1944em;",[579,2890,1100],{"className":2891},[623],[579,2893,2895],{"className":2894},[623],[579,2896,2899],{"className":2897},[2898],"mpunct",",",[579,2901,2903],{"className":2902},[623],"5",[579,2905],{"className":2906,"style":729},[728],[579,2908,650],{"className":2909},[733],[579,2911],{"className":2912,"style":729},[728],[579,2914,2916,2919,2922,2925],{"className":2915},[614],[579,2917],{"className":2918,"style":2834},[618],[579,2920,2609],{"className":2921},[623],[579,2923],{"className":2924,"style":887},[728],[579,2926,2928,2934],{"className":2927},[623],[579,2929,2931],{"className":2930},[623,1536],[579,2932,2399],{"className":2933},[623],[579,2935,2937],{"className":2936},[1104],[579,2938,2940],{"className":2939},[758],[579,2941,2943],{"className":2942},[763],[579,2944,2946],{"className":2945,"style":2834},[767],[579,2947,2948,2951],{"style":2809},[579,2949],{"className":2950,"style":1120},[775],[579,2952,2954],{"className":2953},[1124,1125,1126,1127],[579,2955,660],{"className":2956},[623,1127],[563,2958,2959,2960,2424,3003,3046,3047,3110],{},"Ein dreieckiges Grundstück hat zwei Seiten von ",[579,2961,2963,2982],{"className":2962},[582],[579,2964,2966],{"className":2965},[586],[588,2967,2968],{"xmlns":590},[592,2969,2970,2979],{},[595,2971,2972,2974,2976],{},[655,2973,2903],{},[1398,2975,2396],{},[1398,2977,2978],{},"m",[602,2980,2981],{"encoding":604},"5\\,\\text{m}",[579,2983,2985],{"className":2984,"ariaHidden":610},[609],[579,2986,2988,2991,2994,2997],{"className":2987},[614],[579,2989],{"className":2990,"style":1191},[618],[579,2992,2903],{"className":2993},[623],[579,2995],{"className":2996,"style":887},[728],[579,2998,3000],{"className":2999},[623,1536],[579,3001,2978],{"className":3002},[623],[579,3004,3006,3025],{"className":3005},[582],[579,3007,3009],{"className":3008},[586],[588,3010,3011],{"xmlns":590},[592,3012,3013,3022],{},[595,3014,3015,3018,3020],{},[655,3016,3017],{},"7",[1398,3019,2396],{},[1398,3021,2978],{},[602,3023,3024],{"encoding":604},"7\\,\\text{m}",[579,3026,3028],{"className":3027,"ariaHidden":610},[609],[579,3029,3031,3034,3037,3040],{"className":3030},[614],[579,3032],{"className":3033,"style":1191},[618],[579,3035,3017],{"className":3036},[623],[579,3038],{"className":3039,"style":887},[728],[579,3041,3043],{"className":3042},[623,1536],[579,3044,2978],{"className":3045},[623]," mit einem stumpfen Winkel von ",[579,3048,3050,3069],{"className":3049},[582],[579,3051,3053],{"className":3052},[586],[588,3054,3055],{"xmlns":590},[592,3056,3057,3066],{},[595,3058,3059],{},[1051,3060,3061,3064],{},[655,3062,3063],{},"120",[648,3065,1058],{},[602,3067,3068],{"encoding":604},"120^\\circ",[579,3070,3072],{"className":3071,"ariaHidden":610},[609],[579,3073,3075,3078,3081],{"className":3074},[614],[579,3076],{"className":3077,"style":1089},[618],[579,3079,2609],{"className":3080},[623],[579,3082,3084,3087],{"className":3083},[623],[579,3085,1100],{"className":3086},[623],[579,3088,3090],{"className":3089},[1104],[579,3091,3093],{"className":3092},[758],[579,3094,3096],{"className":3095},[763],[579,3097,3099],{"className":3098,"style":1089},[767],[579,3100,3101,3104],{"style":1116},[579,3102],{"className":3103,"style":1120},[775],[579,3105,3107],{"className":3106},[1124,1125,1126,1127],[579,3108,1058],{"className":3109},[831,1127]," dazwischen:",[579,3112,3114],{"className":3113},[630],[579,3115,3117,3181],{"className":3116},[582],[579,3118,3120],{"className":3119},[586],[588,3121,3122],{"xmlns":590,"display":639},[592,3123,3124,3178],{},[595,3125,3126,3128,3130,3136,3138,3140,3142,3144,3146,3148,3150,3152,3154,3156,3158,3164,3167,3170,3172],{},[598,3127,646],{},[648,3129,650],{},[652,3131,3132,3134],{},[655,3133,657],{},[655,3135,660],{},[648,3137,663],{},[655,3139,2903],{},[1398,3141,2396],{},[1398,3143,2978],{},[648,3145,663],{},[655,3147,3017],{},[1398,3149,2396],{},[1398,3151,2978],{},[648,3153,663],{},[598,3155,676],{},[648,3157,679],{},[1051,3159,3160,3162],{},[655,3161,3063],{},[648,3163,1058],{},[648,3165,3166],{},"≈",[655,3168,3169],{},"15,16",[1398,3171,2396],{},[1051,3173,3174,3176],{},[1398,3175,2978],{},[655,3177,660],{},[602,3179,3180],{"encoding":604},"A = \\frac{1}{2} \\cdot 5\\,\\text{m} \\cdot 7\\,\\text{m} \\cdot \\sin 120^\\circ \\approx 15{,}16\\,\\text{m}^2",[579,3182,3184,3202,3279,3306,3333,3386],{"className":3183,"ariaHidden":610},[609],[579,3185,3187,3190,3193,3196,3199],{"className":3186},[614],[579,3188],{"className":3189,"style":721},[618],[579,3191,646],{"className":3192},[623,624],[579,3194],{"className":3195,"style":729},[728],[579,3197,650],{"className":3198},[733],[579,3200],{"className":3201,"style":729},[728],[579,3203,3205,3208,3270,3273,3276],{"className":3204},[614],[579,3206],{"className":3207,"style":743},[618],[579,3209,3211,3214,3267],{"className":3210},[623],[579,3212],{"className":3213},[750,751],[579,3215,3217],{"className":3216},[652],[579,3218,3220,3259],{"className":3219},[758,759],[579,3221,3223,3256],{"className":3222},[763],[579,3224,3226,3237,3245],{"className":3225,"style":768},[767],[579,3227,3228,3231],{"style":771},[579,3229],{"className":3230,"style":776},[775],[579,3232,3234],{"className":3233},[623],[579,3235,660],{"className":3236},[623],[579,3238,3239,3242],{"style":785},[579,3240],{"className":3241,"style":776},[775],[579,3243],{"className":3244,"style":793},[792],[579,3246,3247,3250],{"style":796},[579,3248],{"className":3249,"style":776},[775],[579,3251,3253],{"className":3252},[623],[579,3254,657],{"className":3255},[623],[579,3257,810],{"className":3258},[809],[579,3260,3262],{"className":3261},[763],[579,3263,3265],{"className":3264,"style":817},[767],[579,3266],{},[579,3268],{"className":3269},[823,751],[579,3271],{"className":3272,"style":827},[728],[579,3274,663],{"className":3275},[831],[579,3277],{"className":3278,"style":827},[728],[579,3280,3282,3285,3288,3291,3297,3300,3303],{"className":3281},[614],[579,3283],{"className":3284,"style":1191},[618],[579,3286,2903],{"className":3287},[623],[579,3289],{"className":3290,"style":887},[728],[579,3292,3294],{"className":3293},[623,1536],[579,3295,2978],{"className":3296},[623],[579,3298],{"className":3299,"style":827},[728],[579,3301,663],{"className":3302},[831],[579,3304],{"className":3305,"style":827},[728],[579,3307,3309,3312,3315,3318,3324,3327,3330],{"className":3308},[614],[579,3310],{"className":3311,"style":1191},[618],[579,3313,3017],{"className":3314},[623],[579,3316],{"className":3317,"style":887},[728],[579,3319,3321],{"className":3320},[623,1536],[579,3322,2978],{"className":3323},[623],[579,3325],{"className":3326,"style":827},[728],[579,3328,663],{"className":3329},[831],[579,3331],{"className":3332,"style":827},[728],[579,3334,3336,3339,3342,3345,3348,3377,3380,3383],{"className":3335},[614],[579,3337],{"className":3338,"style":2779},[618],[579,3340,676],{"className":3341},[883],[579,3343],{"className":3344,"style":887},[728],[579,3346,2609],{"className":3347},[623],[579,3349,3351,3354],{"className":3350},[623],[579,3352,1100],{"className":3353},[623],[579,3355,3357],{"className":3356},[1104],[579,3358,3360],{"className":3359},[758],[579,3361,3363],{"className":3362},[763],[579,3364,3366],{"className":3365,"style":2779},[767],[579,3367,3368,3371],{"style":2809},[579,3369],{"className":3370,"style":1120},[775],[579,3372,3374],{"className":3373},[1124,1125,1126,1127],[579,3375,1058],{"className":3376},[831,1127],[579,3378],{"className":3379,"style":729},[728],[579,3381,3166],{"className":3382},[733],[579,3384],{"className":3385,"style":729},[728],[579,3387,3389,3393,3397,3403,3407,3410],{"className":3388},[614],[579,3390],{"className":3391,"style":3392},[618],"height:1.0585em;vertical-align:-0.1944em;",[579,3394,3396],{"className":3395},[623],"15",[579,3398,3400],{"className":3399},[623],[579,3401,2899],{"className":3402},[2898],[579,3404,3406],{"className":3405},[623],"16",[579,3408],{"className":3409,"style":887},[728],[579,3411,3413,3419],{"className":3412},[623],[579,3414,3416],{"className":3415},[623,1536],[579,3417,2978],{"className":3418},[623],[579,3420,3422],{"className":3421},[1104],[579,3423,3425],{"className":3424},[758],[579,3426,3428],{"className":3427},[763],[579,3429,3431],{"className":3430,"style":2834},[767],[579,3432,3433,3436],{"style":2809},[579,3434],{"className":3435,"style":1120},[775],[579,3437,3439],{"className":3438},[1124,1125,1126,1127],[579,3440,660],{"className":3441},[623,1127],[558,3443,3445],{"id":3444},"typische-fehler","Typische Fehler",[3447,3448,3449,3453,3639],"ul",{},[3450,3451,3452],"li",{},"Einen Winkel verwenden, der nicht zwischen den beiden Seiten liegt.",[3450,3454,3455,3456,3554,3555,3638],{},"Den Faktor ",[579,3457,3459,3477],{"className":3458},[582],[579,3460,3462],{"className":3461},[586],[588,3463,3464],{"xmlns":590},[592,3465,3466,3474],{},[595,3467,3468],{},[652,3469,3470,3472],{},[655,3471,657],{},[655,3473,660],{},[602,3475,3476],{"encoding":604},"\\frac{1}{2}",[579,3478,3480],{"className":3479,"ariaHidden":610},[609],[579,3481,3483,3486],{"className":3482},[614],[579,3484],{"className":3485,"style":1256},[618],[579,3487,3489,3492,3551],{"className":3488},[623],[579,3490],{"className":3491},[750,751],[579,3493,3495],{"className":3494},[652],[579,3496,3498,3543],{"className":3497},[758,759],[579,3499,3501,3540],{"className":3500},[763],[579,3502,3504,3518,3526],{"className":3503,"style":1275},[767],[579,3505,3506,3509],{"style":1278},[579,3507],{"className":3508,"style":776},[775],[579,3510,3512],{"className":3511},[1124,1125,1126,1127],[579,3513,3515],{"className":3514},[623,1127],[579,3516,660],{"className":3517},[623,1127],[579,3519,3520,3523],{"style":785},[579,3521],{"className":3522,"style":776},[775],[579,3524],{"className":3525,"style":793},[792],[579,3527,3528,3531],{"style":1301},[579,3529],{"className":3530,"style":776},[775],[579,3532,3534],{"className":3533},[1124,1125,1126,1127],[579,3535,3537],{"className":3536},[623,1127],[579,3538,657],{"className":3539},[623,1127],[579,3541,810],{"className":3542},[809],[579,3544,3546],{"className":3545},[763],[579,3547,3549],{"className":3548,"style":1323},[767],[579,3550],{},[579,3552],{"className":3553},[823,751]," vergessen: ",[579,3556,3558,3584],{"className":3557},[582],[579,3559,3561],{"className":3560},[586],[588,3562,3563],{"xmlns":590},[592,3564,3565,3581],{},[595,3566,3567,3569,3571,3573,3575,3577,3579],{},[598,3568,695],{},[648,3570,663],{},[598,3572,666],{},[648,3574,663],{},[598,3576,676],{},[648,3578,679],{},[598,3580,600],{},[602,3582,3583],{"encoding":604},"a \\cdot b \\cdot \\sin \\gamma",[579,3585,3587,3605,3623],{"className":3586,"ariaHidden":610},[609],[579,3588,3590,3593,3596,3599,3602],{"className":3589},[614],[579,3591],{"className":3592,"style":860},[618],[579,3594,695],{"className":3595},[623,624],[579,3597],{"className":3598,"style":827},[728],[579,3600,663],{"className":3601},[831],[579,3603],{"className":3604,"style":827},[728],[579,3606,3608,3611,3614,3617,3620],{"className":3607},[614],[579,3609],{"className":3610,"style":841},[618],[579,3612,666],{"className":3613},[623,624],[579,3615],{"className":3616,"style":827},[728],[579,3618,663],{"className":3619},[831],[579,3621],{"className":3622,"style":827},[728],[579,3624,3626,3629,3632,3635],{"className":3625},[614],[579,3627],{"className":3628,"style":1166},[618],[579,3630,676],{"className":3631},[883],[579,3633],{"className":3634,"style":887},[728],[579,3636,600],{"className":3637,"style":625},[623,624]," ist die Fläche eines Parallelogramms, nicht des Dreiecks.",[3450,3640,3641,3642,3714],{},"Bei stumpfen Winkeln an der Formel zweifeln: ",[579,3643,3645,3667],{"className":3644},[582],[579,3646,3648],{"className":3647},[586],[588,3649,3650],{"xmlns":590},[592,3651,3652,3664],{},[595,3653,3654,3656,3658],{},[598,3655,676],{},[648,3657,679],{},[1051,3659,3660,3662],{},[655,3661,3063],{},[648,3663,1058],{},[602,3665,3666],{"encoding":604},"\\sin 120^\\circ",[579,3668,3670],{"className":3669,"ariaHidden":610},[609],[579,3671,3673,3676,3679,3682,3685],{"className":3672},[614],[579,3674],{"className":3675,"style":1089},[618],[579,3677,676],{"className":3678},[883],[579,3680],{"className":3681,"style":887},[728],[579,3683,2609],{"className":3684},[623],[579,3686,3688,3691],{"className":3687},[623],[579,3689,1100],{"className":3690},[623],[579,3692,3694],{"className":3693},[1104],[579,3695,3697],{"className":3696},[758],[579,3698,3700],{"className":3699},[763],[579,3701,3703],{"className":3702,"style":1089},[767],[579,3704,3705,3708],{"style":1116},[579,3706],{"className":3707,"style":1120},[775],[579,3709,3711],{"className":3710},[1124,1125,1126,1127],[579,3712,1058],{"className":3713},[831,1127]," ist positiv, die Formel gilt auch hier.",{"title":3716,"searchDepth":3717,"depth":3717,"links":3718},"",2,[3719,3720,3721,3722],{"id":560,"depth":3717,"text":561},{"id":1368,"depth":3717,"text":1369},{"id":2374,"depth":3717,"text":2375},{"id":3444,"depth":3717,"text":3445},[3724,3727,3730,3732],{"lhs":3725,"rhs":3726},"(2*a^2*b^2 + 2*(a^2 + b^2)*(a^2 + b^2 - 2*a*b*cos(x)) - a^4 - b^4 - (a^2 + b^2 - 2*a*b*cos(x))^2) \u002F 16","(1\u002F2 * a * b * sin(x))^2",{"lhs":3728,"rhs":3729},"1\u002F2 * a * b * sin(pi\u002F2)","a*b\u002F2",{"lhs":3731,"rhs":2609},"1\u002F2 * 6 * 8 * sin(30*pi\u002F180)",{"lhs":3733,"rhs":3734},"round(1\u002F2 * 5 * 7 * sin(120*pi\u002F180), 2)","15.16","\\gamma\\ \\text{ist der Winkel zwischen}\\ a\\ \\text{und}\\ b,\\ 0^\\circ \u003C \\gamma \u003C 180^\\circ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">ist der Winkel zwischen\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo><\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0^\\circ < \\gamma < 180^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7132em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6741em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">18\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3740,"x":3741,"y":3744,"unit":3747,"items":3748},"Dreieck mit den Seiten a und b und dem eingeschlossenen Winkel γ, gestrichelt die Höhe hₐ = b · sin γ",[3742,3743],-0.6,7.9,[3745,3746],-0.9,4.6,36,[3749,3760,3765,3770,3775,3780,3784,3788],{"type":3750,"points":3751,"fill":3759},"polygon",[3752,3755,3757],[3753,3754],4.132,4.096,[3756,3756],0,[3758,3756],7,true,{"type":3761,"from":3762,"to":3763,"style":3764},"segment",[3753,3754],[3753,3756],"dashed",{"type":3766,"at":3767,"from":3768,"to":3769},"rightAngle",[3753,3756],[3756,3756],[3753,3754],{"type":3771,"at":3772,"from":3773,"to":3774,"label":600},"angle",[3758,3756],[3756,3756],[3753,3754],{"type":3776,"at":3777,"text":695},"label",[3778,3779],3.5,-0.45,{"type":3776,"at":3781,"text":666},[3782,3783],5.93,2.31,{"type":3776,"at":3785,"text":1652},[3786,3787],3.7,1.9,{"type":3776,"at":3789,"text":646},[3790,3791],2.6,1,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 306 198\" width=\"306\" height=\"198\" role=\"img\" aria-label=\"Dreieck mit den Seiten a und b und dem eingeschlossenen Winkel γ, gestrichelt die Höhe hₐ = b · sin γ\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-triangle-area-sine-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-triangle-area-sine-clip\">\u003Crect x=\"0\" y=\"0\" width=\"306\" height=\"198\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"170.35,18.14 21.6,165.6 273.6,165.6\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"170.35\" y1=\"18.14\" x2=\"170.35\" y2=\"165.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 158.35 165.6 L 158.35 153.6 L 170.35 153.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"164.35\" cy=\"159.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Cpath d=\"M 273.6 165.6 L 260.98 147.58 A 22 22 0 0 0 251.6 165.6 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"243.44\" y=\"149.9\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">γ\u003C\u002Ftext>\u003Ctext x=\"147.6\" y=\"181.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"235.08\" y=\"82.44\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"154.8\" y=\"97.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003Ctspan class=\"fig-sub\" dy=\"4\">a\u003C\u002Ftspan>\u003C\u002Ftext>\u003Ctext x=\"115.2\" y=\"129.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003C\u002Fsvg>","triangle-area-sine","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{1}{2} \\cdot a \\cdot b \\cdot \\sin \\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8623em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus",[],[3800,3801,3802,3803],"triangle-area","law-of-cosines","law-of-sines","sine-right-triangle",{"title":548,"description":3716},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fflaecheninhalt-dreieck-mit-sinus","Der Flächeninhalt eines Dreiecks ist das halbe Produkt zweier Seiten mal dem Sinus des eingeschlossenen Winkels.",[3808,3809,3810,3811],"flächeninhalt","dreieck","sinus","eingeschlossener winkel",[3813,3816,3820],{"symbol":646,"meaning":3814,"symbolHtml":3815},"Flächeninhalt des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3817,"meaning":3818,"symbolHtml":3819},"a, b","zwei Seiten des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":605,"meaning":3821,"symbolHtml":3822},"Winkel, den die Seiten a und b einschließen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","ka0CEnHBxHNOg-UZ89uBS3DXyj467suzFU2RBYPYBg8",[3825,3828,3831,3834],{"stem":3826,"title":3827,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-dreieck","Flächeninhalt eines Dreiecks",{"stem":3829,"title":3830,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fkosinussatz","Kosinussatz",{"stem":3832,"title":3833,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck","Sinus im rechtwinkligen Dreieck",{"stem":3835,"title":3836,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinussatz","Sinussatz",1793824262381]