[{"data":1,"prerenderedAt":2270},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras":2257},[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":553,"category":247,"checks":2162,"conditions":2167,"conditionsHtml":2168,"deprecated":2169,"description":2156,"extension":2170,"figure":2171,"figureCaption":2172,"figureHtml":2223,"formulaId":2224,"latex":2225,"latexHtml":2226,"level":2227,"meta":2228,"navigation":2189,"path":2229,"redirectFrom":2230,"related":2231,"seo":2236,"stem":2237,"subject":583,"summary":2238,"tags":2239,"variables":2244,"__hash__":2256},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras.md","Satz des Pythagoras",[550,551,552],"Pythagoras","a² + b² = c²","Hypotenuse berechnen",{"type":554,"value":555,"toc":2155},"minimark",[556,561,570,620,623,1010,1014,1156,1542,1662,1945,1949],[557,558,560],"h2",{"id":559},"erklärung","Erklärung",[562,563,564,565,569],"p",{},"Der Satz des Pythagoras gilt ",[566,567,568],"strong",{},"nur in rechtwinkligen Dreiecken",". Er verbindet die drei Seitenlängen: Kennt man zwei davon, kann man die dritte berechnen.",[562,571,572,573,619],{},"Die Hypotenuse ",[574,575,578,600],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,596],"semantics",{},[590,591,592],"mrow",{},[593,594,595],"mi",{},"c",[597,598,595],"annotation",{"encoding":599},"application\u002Fx-tex",[574,601,605],{"className":602,"ariaHidden":604},[603],"katex-html","true",[574,606,609,614],{"className":607},[608],"base",[574,610],{"className":611,"style":613},[612],"strut","height:0.4306em;",[574,615,595],{"className":616},[617,618],"mord","mathnormal"," ist immer die längste Seite und liegt dem rechten Winkel gegenüber.",[562,621,622],{},"Umgestellt nach den einzelnen Seiten:",[574,624,627],{"className":625},[626],"katex-display",[574,628,630,701],{"className":629},[577],[574,631,633],{"className":632},[581],[583,634,636],{"xmlns":585,"display":635},"block",[587,637,638,698],{},[590,639,640,642,646,671,675,677,679],{},[593,641,595],{},[643,644,645],"mo",{},"=",[647,648,649],"msqrt",{},[590,650,651,661,664],{},[652,653,654,657],"msup",{},[593,655,656],{},"a",[658,659,660],"mn",{},"2",[643,662,663],{},"+",[652,665,666,669],{},[593,667,668],{},"b",[658,670,660],{},[672,673],"mspace",{"width":674},"2em",[593,676,656],{},[643,678,645],{},[647,680,681],{},[590,682,683,689,692],{},[652,684,685,687],{},[593,686,595],{},[658,688,660],{},[643,690,691],{},"−",[652,693,694,696],{},[593,695,668],{},[658,697,660],{},[597,699,700],{"encoding":599},"c = \\sqrt{a^2 + b^2}\n\\qquad\na = \\sqrt{c^2 - b^2}",[574,702,704,724,893],{"className":703,"ariaHidden":604},[603],[574,705,707,710,713,717,721],{"className":706},[608],[574,708],{"className":709,"style":613},[612],[574,711,595],{"className":712},[617,618],[574,714],{"className":715,"style":716},[672],"margin-right:0.2778em;",[574,718,645],{"className":719},[720],"mrel",[574,722],{"className":723,"style":716},[672],[574,725,727,731,877,881,884,887,890],{"className":726},[608],[574,728],{"className":729,"style":730},[612],"height:1.24em;vertical-align:-0.1777em;",[574,732,735],{"className":733},[617,734],"sqrt",[574,736,740,868],{"className":737},[738,739],"vlist-t","vlist-t2",[574,741,744,863],{"className":742},[743],"vlist-r",[574,745,749,840],{"className":746,"style":748},[747],"vlist","height:1.0623em;",[574,750,754,759],{"className":751,"style":753},[752],"svg-align","top:-3.2em;",[574,755],{"className":756,"style":758},[757],"pstrut","height:3.2em;",[574,760,763,800,804,808,811],{"className":761,"style":762},[617],"padding-left:1em;",[574,764,766,769],{"className":765},[617],[574,767,656],{"className":768},[617,618],[574,770,773],{"className":771},[772],"msupsub",[574,774,776],{"className":775},[738],[574,777,779],{"className":778},[743],[574,780,783],{"className":781,"style":782},[747],"height:0.7401em;",[574,784,786,790],{"style":785},"top:-2.989em;margin-right:0.05em;",[574,787],{"className":788,"style":789},[757],"height:2.7em;",[574,791,797],{"className":792},[793,794,795,796],"sizing","reset-size6","size3","mtight",[574,798,660],{"className":799},[617,796],[574,801],{"className":802,"style":803},[672],"margin-right:0.2222em;",[574,805,663],{"className":806},[807],"mbin",[574,809],{"className":810,"style":803},[672],[574,812,814,817],{"className":813},[617],[574,815,668],{"className":816},[617,618],[574,818,820],{"className":819},[772],[574,821,823],{"className":822},[738],[574,824,826],{"className":825},[743],[574,827,829],{"className":828,"style":782},[747],[574,830,831,834],{"style":785},[574,832],{"className":833,"style":789},[757],[574,835,837],{"className":836},[793,794,795,796],[574,838,660],{"className":839},[617,796],[574,841,843,846],{"style":842},"top:-3.0223em;",[574,844],{"className":845,"style":758},[757],[574,847,851],{"className":848,"style":850},[849],"hide-tail","min-width:1.02em;height:1.28em;",[852,853,859],"svg",{"xmlns":854,"width":855,"height":856,"viewBox":857,"preserveAspectRatio":858},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[860,861],"path",{"d":862},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[574,864,867],{"className":865},[866],"vlist-s","​",[574,869,871],{"className":870},[743],[574,872,875],{"className":873,"style":874},[747],"height:0.1777em;",[574,876],{},[574,878],{"className":879,"style":880},[672],"margin-right:2em;",[574,882,656],{"className":883},[617,618],[574,885],{"className":886,"style":716},[672],[574,888,645],{"className":889},[720],[574,891],{"className":892,"style":716},[672],[574,894,896,899],{"className":895},[608],[574,897],{"className":898,"style":730},[612],[574,900,902],{"className":901},[617,734],[574,903,905,1002],{"className":904},[738,739],[574,906,908,999],{"className":907},[743],[574,909,911,987],{"className":910,"style":748},[747],[574,912,914,917],{"className":913,"style":753},[752],[574,915],{"className":916,"style":758},[757],[574,918,920,949,952,955,958],{"className":919,"style":762},[617],[574,921,923,926],{"className":922},[617],[574,924,595],{"className":925},[617,618],[574,927,929],{"className":928},[772],[574,930,932],{"className":931},[738],[574,933,935],{"className":934},[743],[574,936,938],{"className":937,"style":782},[747],[574,939,940,943],{"style":785},[574,941],{"className":942,"style":789},[757],[574,944,946],{"className":945},[793,794,795,796],[574,947,660],{"className":948},[617,796],[574,950],{"className":951,"style":803},[672],[574,953,691],{"className":954},[807],[574,956],{"className":957,"style":803},[672],[574,959,961,964],{"className":960},[617],[574,962,668],{"className":963},[617,618],[574,965,967],{"className":966},[772],[574,968,970],{"className":969},[738],[574,971,973],{"className":972},[743],[574,974,976],{"className":975,"style":782},[747],[574,977,978,981],{"style":785},[574,979],{"className":980,"style":789},[757],[574,982,984],{"className":983},[793,794,795,796],[574,985,660],{"className":986},[617,796],[574,988,989,992],{"style":842},[574,990],{"className":991,"style":758},[757],[574,993,995],{"className":994,"style":850},[849],[852,996,997],{"xmlns":854,"width":855,"height":856,"viewBox":857,"preserveAspectRatio":858},[860,998],{"d":862},[574,1000,867],{"className":1001},[866],[574,1003,1005],{"className":1004},[743],[574,1006,1008],{"className":1007,"style":874},[747],[574,1009],{},[557,1011,1013],{"id":1012},"beispiele","Beispiele",[562,1015,1016,1017,1088,1089,1155],{},"Ein rechtwinkliges Dreieck hat die Katheten ",[574,1018,1020,1046],{"className":1019},[577],[574,1021,1023],{"className":1022},[581],[583,1024,1025],{"xmlns":585},[587,1026,1027,1043],{},[590,1028,1029,1031,1033,1036,1040],{},[593,1030,656],{},[643,1032,645],{},[658,1034,1035],{},"3",[1037,1038,1039],"mtext",{}," ",[1037,1041,1042],{},"cm",[597,1044,1045],{"encoding":599},"a = 3\\,\\text{cm}",[574,1047,1049,1067],{"className":1048,"ariaHidden":604},[603],[574,1050,1052,1055,1058,1061,1064],{"className":1051},[608],[574,1053],{"className":1054,"style":613},[612],[574,1056,656],{"className":1057},[617,618],[574,1059],{"className":1060,"style":716},[672],[574,1062,645],{"className":1063},[720],[574,1065],{"className":1066,"style":716},[672],[574,1068,1070,1074,1077,1081],{"className":1069},[608],[574,1071],{"className":1072,"style":1073},[612],"height:0.6444em;",[574,1075,1035],{"className":1076},[617],[574,1078],{"className":1079,"style":1080},[672],"margin-right:0.1667em;",[574,1082,1085],{"className":1083},[617,1084],"text",[574,1086,1042],{"className":1087},[617]," und ",[574,1090,1092,1115],{"className":1091},[577],[574,1093,1095],{"className":1094},[581],[583,1096,1097],{"xmlns":585},[587,1098,1099,1112],{},[590,1100,1101,1103,1105,1108,1110],{},[593,1102,668],{},[643,1104,645],{},[658,1106,1107],{},"4",[1037,1109,1039],{},[1037,1111,1042],{},[597,1113,1114],{"encoding":599},"b = 4\\,\\text{cm}",[574,1116,1118,1137],{"className":1117,"ariaHidden":604},[603],[574,1119,1121,1125,1128,1131,1134],{"className":1120},[608],[574,1122],{"className":1123,"style":1124},[612],"height:0.6944em;",[574,1126,668],{"className":1127},[617,618],[574,1129],{"className":1130,"style":716},[672],[574,1132,645],{"className":1133},[720],[574,1135],{"className":1136,"style":716},[672],[574,1138,1140,1143,1146,1149],{"className":1139},[608],[574,1141],{"className":1142,"style":1073},[612],[574,1144,1107],{"className":1145},[617],[574,1147],{"className":1148,"style":1080},[672],[574,1150,1152],{"className":1151},[617,1084],[574,1153,1042],{"className":1154},[617],":",[574,1157,1159],{"className":1158},[626],[574,1160,1162,1226],{"className":1161},[577],[574,1163,1165],{"className":1164},[581],[583,1166,1167],{"xmlns":585,"display":635},[587,1168,1169,1223],{},[590,1170,1171,1173,1175,1193,1195,1207,1209,1214,1216,1219,1221],{},[593,1172,595],{},[643,1174,645],{},[647,1176,1177],{},[590,1178,1179,1185,1187],{},[652,1180,1181,1183],{},[658,1182,1035],{},[658,1184,660],{},[643,1186,663],{},[652,1188,1189,1191],{},[658,1190,1107],{},[658,1192,660],{},[643,1194,645],{},[647,1196,1197],{},[590,1198,1199,1202,1204],{},[658,1200,1201],{},"9",[643,1203,663],{},[658,1205,1206],{},"16",[643,1208,645],{},[647,1210,1211],{},[658,1212,1213],{},"25",[643,1215,645],{},[658,1217,1218],{},"5",[1037,1220,1039],{},[1037,1222,1042],{},[597,1224,1225],{"encoding":599},"c = \\sqrt{3^2 + 4^2} = \\sqrt{9 + 16} = \\sqrt{25} = 5\\,\\text{cm}",[574,1227,1229,1247,1373,1458,1524],{"className":1228,"ariaHidden":604},[603],[574,1230,1232,1235,1238,1241,1244],{"className":1231},[608],[574,1233],{"className":1234,"style":613},[612],[574,1236,595],{"className":1237},[617,618],[574,1239],{"className":1240,"style":716},[672],[574,1242,645],{"className":1243},[720],[574,1245],{"className":1246,"style":716},[672],[574,1248,1250,1253,1364,1367,1370],{"className":1249},[608],[574,1251],{"className":1252,"style":730},[612],[574,1254,1256],{"className":1255},[617,734],[574,1257,1259,1356],{"className":1258},[738,739],[574,1260,1262,1353],{"className":1261},[743],[574,1263,1265,1341],{"className":1264,"style":748},[747],[574,1266,1268,1271],{"className":1267,"style":753},[752],[574,1269],{"className":1270,"style":758},[757],[574,1272,1274,1303,1306,1309,1312],{"className":1273,"style":762},[617],[574,1275,1277,1280],{"className":1276},[617],[574,1278,1035],{"className":1279},[617],[574,1281,1283],{"className":1282},[772],[574,1284,1286],{"className":1285},[738],[574,1287,1289],{"className":1288},[743],[574,1290,1292],{"className":1291,"style":782},[747],[574,1293,1294,1297],{"style":785},[574,1295],{"className":1296,"style":789},[757],[574,1298,1300],{"className":1299},[793,794,795,796],[574,1301,660],{"className":1302},[617,796],[574,1304],{"className":1305,"style":803},[672],[574,1307,663],{"className":1308},[807],[574,1310],{"className":1311,"style":803},[672],[574,1313,1315,1318],{"className":1314},[617],[574,1316,1107],{"className":1317},[617],[574,1319,1321],{"className":1320},[772],[574,1322,1324],{"className":1323},[738],[574,1325,1327],{"className":1326},[743],[574,1328,1330],{"className":1329,"style":782},[747],[574,1331,1332,1335],{"style":785},[574,1333],{"className":1334,"style":789},[757],[574,1336,1338],{"className":1337},[793,794,795,796],[574,1339,660],{"className":1340},[617,796],[574,1342,1343,1346],{"style":842},[574,1344],{"className":1345,"style":758},[757],[574,1347,1349],{"className":1348,"style":850},[849],[852,1350,1351],{"xmlns":854,"width":855,"height":856,"viewBox":857,"preserveAspectRatio":858},[860,1352],{"d":862},[574,1354,867],{"className":1355},[866],[574,1357,1359],{"className":1358},[743],[574,1360,1362],{"className":1361,"style":874},[747],[574,1363],{},[574,1365],{"className":1366,"style":716},[672],[574,1368,645],{"className":1369},[720],[574,1371],{"className":1372,"style":716},[672],[574,1374,1376,1380,1449,1452,1455],{"className":1375},[608],[574,1377],{"className":1378,"style":1379},[612],"height:1.04em;vertical-align:-0.1256em;",[574,1381,1383],{"className":1382},[617,734],[574,1384,1386,1440],{"className":1385},[738,739],[574,1387,1389,1437],{"className":1388},[743],[574,1390,1393,1420],{"className":1391,"style":1392},[747],"height:0.9144em;",[574,1394,1397,1401],{"className":1395,"style":1396},[752],"top:-3em;",[574,1398],{"className":1399,"style":1400},[757],"height:3em;",[574,1402,1405,1408,1411,1414,1417],{"className":1403,"style":1404},[617],"padding-left:0.833em;",[574,1406,1201],{"className":1407},[617],[574,1409],{"className":1410,"style":803},[672],[574,1412,663],{"className":1413},[807],[574,1415],{"className":1416,"style":803},[672],[574,1418,1206],{"className":1419},[617],[574,1421,1423,1426],{"style":1422},"top:-2.8744em;",[574,1424],{"className":1425,"style":1400},[757],[574,1427,1430],{"className":1428,"style":1429},[849],"min-width:0.853em;height:1.08em;",[852,1431,1434],{"xmlns":854,"width":855,"height":1432,"viewBox":1433,"preserveAspectRatio":858},"1.08em","0 0 400000 1080",[860,1435],{"d":1436},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[574,1438,867],{"className":1439},[866],[574,1441,1443],{"className":1442},[743],[574,1444,1447],{"className":1445,"style":1446},[747],"height:0.1256em;",[574,1448],{},[574,1450],{"className":1451,"style":716},[672],[574,1453,645],{"className":1454},[720],[574,1456],{"className":1457,"style":716},[672],[574,1459,1461,1465,1515,1518,1521],{"className":1460},[608],[574,1462],{"className":1463,"style":1464},[612],"height:1.04em;vertical-align:-0.0839em;",[574,1466,1468],{"className":1467},[617,734],[574,1469,1471,1506],{"className":1470},[738,739],[574,1472,1474,1503],{"className":1473},[743],[574,1475,1478,1490],{"className":1476,"style":1477},[747],"height:0.9561em;",[574,1479,1481,1484],{"className":1480,"style":1396},[752],[574,1482],{"className":1483,"style":1400},[757],[574,1485,1487],{"className":1486,"style":1404},[617],[574,1488,1213],{"className":1489},[617],[574,1491,1493,1496],{"style":1492},"top:-2.9161em;",[574,1494],{"className":1495,"style":1400},[757],[574,1497,1499],{"className":1498,"style":1429},[849],[852,1500,1501],{"xmlns":854,"width":855,"height":1432,"viewBox":1433,"preserveAspectRatio":858},[860,1502],{"d":1436},[574,1504,867],{"className":1505},[866],[574,1507,1509],{"className":1508},[743],[574,1510,1513],{"className":1511,"style":1512},[747],"height:0.0839em;",[574,1514],{},[574,1516],{"className":1517,"style":716},[672],[574,1519,645],{"className":1520},[720],[574,1522],{"className":1523,"style":716},[672],[574,1525,1527,1530,1533,1536],{"className":1526},[608],[574,1528],{"className":1529,"style":1073},[612],[574,1531,1218],{"className":1532},[617],[574,1534],{"className":1535,"style":1080},[672],[574,1537,1539],{"className":1538},[617,1084],[574,1540,1042],{"className":1541},[617],[562,1543,1544,1545,1574,1575,1088,1619,1155],{},"Die Diagonale ",[574,1546,1548,1562],{"className":1547},[577],[574,1549,1551],{"className":1550},[581],[583,1552,1553],{"xmlns":585},[587,1554,1555,1560],{},[590,1556,1557],{},[593,1558,1559],{},"d",[597,1561,1559],{"encoding":599},[574,1563,1565],{"className":1564,"ariaHidden":604},[603],[574,1566,1568,1571],{"className":1567},[608],[574,1569],{"className":1570,"style":1124},[612],[574,1572,1559],{"className":1573},[617,618]," eines Rechtecks mit den Seiten ",[574,1576,1578,1598],{"className":1577},[577],[574,1579,1581],{"className":1580},[581],[583,1582,1583],{"xmlns":585},[587,1584,1585,1595],{},[590,1586,1587,1590,1592],{},[658,1588,1589],{},"6",[1037,1591,1039],{},[1037,1593,1594],{},"m",[597,1596,1597],{"encoding":599},"6\\,\\text{m}",[574,1599,1601],{"className":1600,"ariaHidden":604},[603],[574,1602,1604,1607,1610,1613],{"className":1603},[608],[574,1605],{"className":1606,"style":1073},[612],[574,1608,1589],{"className":1609},[617],[574,1611],{"className":1612,"style":1080},[672],[574,1614,1616],{"className":1615},[617,1084],[574,1617,1594],{"className":1618},[617],[574,1620,1622,1641],{"className":1621},[577],[574,1623,1625],{"className":1624},[581],[583,1626,1627],{"xmlns":585},[587,1628,1629,1638],{},[590,1630,1631,1634,1636],{},[658,1632,1633],{},"8",[1037,1635,1039],{},[1037,1637,1594],{},[597,1639,1640],{"encoding":599},"8\\,\\text{m}",[574,1642,1644],{"className":1643,"ariaHidden":604},[603],[574,1645,1647,1650,1653,1656],{"className":1646},[608],[574,1648],{"className":1649,"style":1073},[612],[574,1651,1633],{"className":1652},[617],[574,1654],{"className":1655,"style":1080},[672],[574,1657,1659],{"className":1658},[617,1084],[574,1660,1594],{"className":1661},[617],[574,1663,1665],{"className":1664},[626],[574,1666,1668,1718],{"className":1667},[577],[574,1669,1671],{"className":1670},[581],[583,1672,1673],{"xmlns":585,"display":635},[587,1674,1675,1715],{},[590,1676,1677,1679,1681,1699,1701,1706,1708,1711,1713],{},[593,1678,1559],{},[643,1680,645],{},[647,1682,1683],{},[590,1684,1685,1691,1693],{},[652,1686,1687,1689],{},[658,1688,1589],{},[658,1690,660],{},[643,1692,663],{},[652,1694,1695,1697],{},[658,1696,1633],{},[658,1698,660],{},[643,1700,645],{},[647,1702,1703],{},[658,1704,1705],{},"100",[643,1707,645],{},[658,1709,1710],{},"10",[1037,1712,1039],{},[1037,1714,1594],{},[597,1716,1717],{"encoding":599},"d = \\sqrt{6^2 + 8^2} = \\sqrt{100} = 10\\,\\text{m}",[574,1719,1721,1739,1865,1927],{"className":1720,"ariaHidden":604},[603],[574,1722,1724,1727,1730,1733,1736],{"className":1723},[608],[574,1725],{"className":1726,"style":1124},[612],[574,1728,1559],{"className":1729},[617,618],[574,1731],{"className":1732,"style":716},[672],[574,1734,645],{"className":1735},[720],[574,1737],{"className":1738,"style":716},[672],[574,1740,1742,1745,1856,1859,1862],{"className":1741},[608],[574,1743],{"className":1744,"style":730},[612],[574,1746,1748],{"className":1747},[617,734],[574,1749,1751,1848],{"className":1750},[738,739],[574,1752,1754,1845],{"className":1753},[743],[574,1755,1757,1833],{"className":1756,"style":748},[747],[574,1758,1760,1763],{"className":1759,"style":753},[752],[574,1761],{"className":1762,"style":758},[757],[574,1764,1766,1795,1798,1801,1804],{"className":1765,"style":762},[617],[574,1767,1769,1772],{"className":1768},[617],[574,1770,1589],{"className":1771},[617],[574,1773,1775],{"className":1774},[772],[574,1776,1778],{"className":1777},[738],[574,1779,1781],{"className":1780},[743],[574,1782,1784],{"className":1783,"style":782},[747],[574,1785,1786,1789],{"style":785},[574,1787],{"className":1788,"style":789},[757],[574,1790,1792],{"className":1791},[793,794,795,796],[574,1793,660],{"className":1794},[617,796],[574,1796],{"className":1797,"style":803},[672],[574,1799,663],{"className":1800},[807],[574,1802],{"className":1803,"style":803},[672],[574,1805,1807,1810],{"className":1806},[617],[574,1808,1633],{"className":1809},[617],[574,1811,1813],{"className":1812},[772],[574,1814,1816],{"className":1815},[738],[574,1817,1819],{"className":1818},[743],[574,1820,1822],{"className":1821,"style":782},[747],[574,1823,1824,1827],{"style":785},[574,1825],{"className":1826,"style":789},[757],[574,1828,1830],{"className":1829},[793,794,795,796],[574,1831,660],{"className":1832},[617,796],[574,1834,1835,1838],{"style":842},[574,1836],{"className":1837,"style":758},[757],[574,1839,1841],{"className":1840,"style":850},[849],[852,1842,1843],{"xmlns":854,"width":855,"height":856,"viewBox":857,"preserveAspectRatio":858},[860,1844],{"d":862},[574,1846,867],{"className":1847},[866],[574,1849,1851],{"className":1850},[743],[574,1852,1854],{"className":1853,"style":874},[747],[574,1855],{},[574,1857],{"className":1858,"style":716},[672],[574,1860,645],{"className":1861},[720],[574,1863],{"className":1864,"style":716},[672],[574,1866,1868,1871,1918,1921,1924],{"className":1867},[608],[574,1869],{"className":1870,"style":1464},[612],[574,1872,1874],{"className":1873},[617,734],[574,1875,1877,1910],{"className":1876},[738,739],[574,1878,1880,1907],{"className":1879},[743],[574,1881,1883,1895],{"className":1882,"style":1477},[747],[574,1884,1886,1889],{"className":1885,"style":1396},[752],[574,1887],{"className":1888,"style":1400},[757],[574,1890,1892],{"className":1891,"style":1404},[617],[574,1893,1705],{"className":1894},[617],[574,1896,1897,1900],{"style":1492},[574,1898],{"className":1899,"style":1400},[757],[574,1901,1903],{"className":1902,"style":1429},[849],[852,1904,1905],{"xmlns":854,"width":855,"height":1432,"viewBox":1433,"preserveAspectRatio":858},[860,1906],{"d":1436},[574,1908,867],{"className":1909},[866],[574,1911,1913],{"className":1912},[743],[574,1914,1916],{"className":1915,"style":1512},[747],[574,1917],{},[574,1919],{"className":1920,"style":716},[672],[574,1922,645],{"className":1923},[720],[574,1925],{"className":1926,"style":716},[672],[574,1928,1930,1933,1936,1939],{"className":1929},[608],[574,1931],{"className":1932,"style":1073},[612],[574,1934,1710],{"className":1935},[617],[574,1937],{"className":1938,"style":1080},[672],[574,1940,1942],{"className":1941},[617,1084],[574,1943,1594],{"className":1944},[617],[557,1946,1948],{"id":1947},"typische-fehler","Typische Fehler",[1950,1951,1952,1956,2016],"ul",{},[1953,1954,1955],"li",{},"Die Formel in nicht rechtwinkligen Dreiecken anwenden.",[1953,1957,1958,1986,1987,2015],{},[574,1959,1961,1974],{"className":1960},[577],[574,1962,1964],{"className":1963},[581],[583,1965,1966],{"xmlns":585},[587,1967,1968,1972],{},[590,1969,1970],{},[593,1971,595],{},[597,1973,595],{"encoding":599},[574,1975,1977],{"className":1976,"ariaHidden":604},[603],[574,1978,1980,1983],{"className":1979},[608],[574,1981],{"className":1982,"style":613},[612],[574,1984,595],{"className":1985},[617,618]," mit einer Kathete verwechseln: ",[574,1988,1990,2003],{"className":1989},[577],[574,1991,1993],{"className":1992},[581],[583,1994,1995],{"xmlns":585},[587,1996,1997,2001],{},[590,1998,1999],{},[593,2000,595],{},[597,2002,595],{"encoding":599},[574,2004,2006],{"className":2005,"ariaHidden":604},[603],[574,2007,2009,2012],{"className":2008},[608],[574,2010],{"className":2011,"style":613},[612],[574,2013,595],{"className":2014},[617,618]," ist immer die Seite gegenüber dem rechten Winkel.",[1953,2017,2018,2019,2102,2103,2154],{},"Am Ende die Wurzel vergessen: ",[574,2020,2022,2044],{"className":2021},[577],[574,2023,2025],{"className":2024},[581],[583,2026,2027],{"xmlns":585},[587,2028,2029,2041],{},[590,2030,2031,2037,2039],{},[652,2032,2033,2035],{},[593,2034,595],{},[658,2036,660],{},[643,2038,645],{},[658,2040,1213],{},[597,2042,2043],{"encoding":599},"c^2 = 25",[574,2045,2047,2093],{"className":2046,"ariaHidden":604},[603],[574,2048,2050,2054,2084,2087,2090],{"className":2049},[608],[574,2051],{"className":2052,"style":2053},[612],"height:0.8141em;",[574,2055,2057,2060],{"className":2056},[617],[574,2058,595],{"className":2059},[617,618],[574,2061,2063],{"className":2062},[772],[574,2064,2066],{"className":2065},[738],[574,2067,2069],{"className":2068},[743],[574,2070,2072],{"className":2071,"style":2053},[747],[574,2073,2075,2078],{"style":2074},"top:-3.063em;margin-right:0.05em;",[574,2076],{"className":2077,"style":789},[757],[574,2079,2081],{"className":2080},[793,794,795,796],[574,2082,660],{"className":2083},[617,796],[574,2085],{"className":2086,"style":716},[672],[574,2088,645],{"className":2089},[720],[574,2091],{"className":2092,"style":716},[672],[574,2094,2096,2099],{"className":2095},[608],[574,2097],{"className":2098,"style":1073},[612],[574,2100,1213],{"className":2101},[617]," heißt ",[574,2104,2106,2124],{"className":2105},[577],[574,2107,2109],{"className":2108},[581],[583,2110,2111],{"xmlns":585},[587,2112,2113,2121],{},[590,2114,2115,2117,2119],{},[593,2116,595],{},[643,2118,645],{},[658,2120,1218],{},[597,2122,2123],{"encoding":599},"c = 5",[574,2125,2127,2145],{"className":2126,"ariaHidden":604},[603],[574,2128,2130,2133,2136,2139,2142],{"className":2129},[608],[574,2131],{"className":2132,"style":613},[612],[574,2134,595],{"className":2135},[617,618],[574,2137],{"className":2138,"style":716},[672],[574,2140,645],{"className":2141},[720],[574,2143],{"className":2144,"style":716},[672],[574,2146,2148,2151],{"className":2147},[608],[574,2149],{"className":2150,"style":1073},[612],[574,2152,1218],{"className":2153},[617],".",{"title":2156,"searchDepth":2157,"depth":2157,"links":2158},"",2,[2159,2160,2161],{"id":559,"depth":2157,"text":560},{"id":1012,"depth":2157,"text":1013},{"id":1947,"depth":2157,"text":1948},[2163,2165],{"lhs":2164,"rhs":1218},"sqrt(3^2 + 4^2)",{"lhs":2166,"rhs":1710},"sqrt(6^2 + 8^2)","\\gamma = 90^\\circ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma = 90^\\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:0.625em;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\">9\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":2172,"x":2173,"y":2176,"items":2179},"Rechtwinkliges Dreieck mit den Katheten a und b und der Hypotenuse c",[2174,2175],-0.9,4.8,[2177,2178],-0.8,3.6,[2180,2190,2195,2199,2202,2206,2213,2218],{"type":2181,"points":2182,"fill":2189},"polygon",[2183,2185,2187],[2184,2184],0,[2186,2184],4,[2184,2188],3,true,{"type":2191,"at":2192,"from":2193,"to":2194},"rightAngle",[2184,2184],[2186,2184],[2184,2188],{"type":2196,"at":2197,"text":656},"label",[2157,2198],-0.4,{"type":2196,"at":2200,"text":668},[2198,2201],1.5,{"type":2196,"at":2203,"text":595},[2204,2205],2.3,1.85,{"type":2207,"at":2208,"label":2209,"offset":2210},"point",[2184,2184],"C",[2211,2212],-18,12,{"type":2207,"at":2214,"label":2215,"offset":2216},[2186,2184],"B",[2217,2212],6,{"type":2207,"at":2219,"label":2220,"offset":2221},[2184,2188],"A",[2211,2222],-4,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 273.6 211.2\" width=\"273.6\" height=\"211.2\" role=\"img\" aria-label=\"Rechtwinkliges Dreieck mit den Katheten a und b und der Hypotenuse c\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-pythagorean-theorem-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-pythagorean-theorem-clip\">\u003Crect x=\"0\" y=\"0\" width=\"273.6\" height=\"211.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"43.2,172.8 235.2,172.8 43.2,28.8\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 55.2 172.8 L 55.2 160.8 L 43.2 160.8\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"49.2\" cy=\"166.8\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"139.2\" y=\"192\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"24\" y=\"100.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"153.6\" y=\"84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ccircle cx=\"43.2\" cy=\"172.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"25.200000000000003\" y=\"184.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003Ccircle cx=\"235.2\" cy=\"172.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"241.2\" y=\"184.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"43.2\" cy=\"28.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"25.200000000000003\" y=\"24.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003C\u002Fsvg>","pythagorean-theorem","a^2 + b^2 = c^2","\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>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a^2 + b^2 = c^2\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:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\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:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras",[],[2232,2233,2234,2235],"altitude-theorem","leg-theorem","distance-two-points","pythagorean-identity",{"title":548,"description":2156},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Im rechtwinkligen Dreieck ist die Summe der Kathetenquadrate gleich dem Hypotenusenquadrat.",[2240,2241,2242,2243],"rechtwinkliges dreieck","hypotenuse","kathete","seitenlänge",[2245,2249,2252],{"symbol":2246,"meaning":2247,"symbolHtml":2248},"a, b","Katheten, die beiden Seiten am rechten Winkel","\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":595,"meaning":2250,"symbolHtml":2251},"Hypotenuse, die Seite gegenüber dem rechten Winkel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\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\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2253,"meaning":2254,"symbolHtml":2255},"\\gamma","Winkel gegenüber von c (der rechte Winkel)","\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>","914U5b5Yr0Q4MCAUEu5xARfittpUVQQPWyVgeyugsU4",[2258,2261,2264,2267],{"stem":2259,"title":2260,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fabstand-zweier-punkte","Abstand zweier Punkte",{"stem":2262,"title":2263,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fhoehensatz","Höhensatz",{"stem":2265,"title":2266,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkathetensatz","Kathetensatz",{"stem":2268,"title":2269,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftrigonometrischer-pythagoras","Trigonometrischer Pythagoras",1793824269823]