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",[578,1116,1118,1131],{"className":1117},[581],[578,1119,1121],{"className":1120},[585],[587,1122,1123],{"xmlns":589},[591,1124,1125,1129],{},[594,1126,1127],{},[692,1128,744],{},[601,1130,744],{"encoding":603},[578,1132,1134],{"className":1133,"ariaHidden":609},[608],[578,1135,1137,1141],{"className":1136},[613],[578,1138],{"className":1139,"style":1140},[617],"height:0.6444em;",[578,1142,744],{"className":1143},[622],[578,1145,1147,1161],{"className":1146},[581],[578,1148,1150],{"className":1149},[585],[587,1151,1152],{"xmlns":589},[591,1153,1154,1159],{},[594,1155,1156],{},[692,1157,1158],{},"1",[601,1160,1158],{"encoding":603},[578,1162,1164],{"className":1163,"ariaHidden":609},[608],[578,1165,1167,1170],{"className":1166},[613],[578,1168],{"className":1169,"style":1140},[617],[578,1171,1158],{"className":1172},[622],". Umgestellt erhält man:",[578,1175,1178],{"className":1176},[1177],"katex-display",[578,1179,1181,1229],{"className":1180},[581],[578,1182,1184],{"className":1183},[585],[587,1185,1187],{"xmlns":589,"display":1186},"block",[591,1188,1189,1226],{},[594,1190,1191,1194,1196,1198,1201,1203,1205,1207,1210,1212,1214],{},[1192,1193,628],"mtext",{},[685,1195,687],{},[1192,1197,661],{},[685,1199,1200],{},"⋅",[597,1202,795],{},[685,1204,798],{},[597,1206,599],{},[718,1208],{"width":1209},"2em",[1192,1211,661],{},[685,1213,687],{},[804,1215,1216,1218],{},[1192,1217,628],{},[594,1219,1220,1222,1224],{},[597,1221,795],{},[685,1223,798],{},[597,1225,599],{},[601,1227,1228],{"encoding":603},"\\text{Gegenkathete} = \\text{Hypotenuse} \\cdot \\sin \\alpha\n\\qquad\n\\text{Hypotenuse} = \\frac{\\text{Gegenkathete}}{\\sin \\alpha}",[578,1230,1232,1254,1277,1311],{"className":1231,"ariaHidden":609},[608],[578,1233,1235,1238,1245,1248,1251],{"className":1234},[613],[578,1236],{"className":1237,"style":975},[617],[578,1239,1242],{"className":1240},[622,1241],"text",[578,1243,628],{"className":1244},[622],[578,1246],{"className":1247,"style":719},[718],[578,1249,687],{"className":1250},[723],[578,1252],{"className":1253,"style":719},[718],[578,1255,1257,1261,1267,1271,1274],{"className":1256},[613],[578,1258],{"className":1259,"style":1260},[617],"height:0.8778em;vertical-align:-0.1944em;",[578,1262,1264],{"className":1263},[622,1241],[578,1265,661],{"className":1266},[622],[578,1268],{"className":1269,"style":1270},[718],"margin-right:0.2222em;",[578,1272,1200],{"className":1273},[779],[578,1275],{"className":1276,"style":1270},[718],[578,1278,1280,1283,1286,1289,1292,1296,1302,1305,1308],{"className":1279},[613],[578,1281],{"className":1282,"style":1260},[617],[578,1284,795],{"className":1285},[828],[578,1287],{"className":1288,"style":832},[718],[578,1290,599],{"className":1291,"style":624},[622,623],[578,1293],{"className":1294,"style":1295},[718],"margin-right:2em;",[578,1297,1299],{"className":1298},[622,1241],[578,1300,661],{"className":1301},[622],[578,1303],{"className":1304,"style":719},[718],[578,1306,687],{"className":1307},[723],[578,1309],{"className":1310,"style":719},[718],[578,1312,1314,1318],{"className":1313},[613],[578,1315],{"className":1316,"style":1317},[617],"height:2.0574em;vertical-align:-0.686em;",[578,1319,1321,1324,1390],{"className":1320},[622],[578,1322],{"className":1323},[858,859],[578,1325,1327],{"className":1326},[804],[578,1328,1330,1381],{"className":1329},[752,866],[578,1331,1333,1378],{"className":1332},[756],[578,1334,1337,1355,1363],{"className":1335,"style":1336},[760],"height:1.3714em;",[578,1338,1340,1343],{"style":1339},"top:-2.314em;",[578,1341],{"className":1342,"style":880},[767],[578,1344,1346,1349,1352],{"className":1345},[622],[578,1347,795],{"className":1348},[828],[578,1350],{"className":1351,"style":832},[718],[578,1353,599],{"className":1354,"style":624},[622,623],[578,1356,1357,1360],{"style":892},[578,1358],{"className":1359,"style":880},[767],[578,1361],{"className":1362,"style":900},[899],[578,1364,1366,1369],{"style":1365},"top:-3.677em;",[578,1367],{"className":1368,"style":880},[767],[578,1370,1372],{"className":1371},[622],[578,1373,1375],{"className":1374},[622,1241],[578,1376,628],{"className":1377},[622],[578,1379,920],{"className":1380},[919],[578,1382,1384],{"className":1383},[756],[578,1385,1388],{"className":1386,"style":1387},[760],"height:0.686em;",[578,1389],{},[578,1391],{"className":1392},[933,859],[565,1394,1395,1396,1472,1473,1477,1478,1480],{},"Den Winkel selbst bekommt man mit der Umkehrfunktion ",[578,1397,1399,1426],{"className":1398},[581],[578,1400,1402],{"className":1401},[585],[587,1403,1404],{"xmlns":589},[591,1405,1406,1423],{},[594,1407,1408],{},[689,1409,1410,1416],{},[594,1411,1412,1414],{},[597,1413,795],{},[685,1415,798],{},[594,1417,1418,1421],{},[685,1419,1420],{},"−",[692,1422,1158],{},[601,1424,1425],{"encoding":603},"\\sin^{-1}",[578,1427,1429],{"className":1428,"ariaHidden":609},[608],[578,1430,1432,1436],{"className":1431},[613],[578,1433],{"className":1434,"style":1435},[617],"height:0.8719em;",[578,1437,1439,1442],{"className":1438},[828],[578,1440,795],{"className":1441},[828],[578,1443,1445],{"className":1444},[748],[578,1446,1448],{"className":1447},[752],[578,1449,1451],{"className":1450},[756],[578,1452,1454],{"className":1453,"style":1435},[760],[578,1455,1457,1460],{"style":1456},"top:-3.1208em;margin-right:0.05em;",[578,1458],{"className":1459,"style":768},[767],[578,1461,1463],{"className":1462},[772,773,774,775],[578,1464,1466,1469],{"className":1465},[622,775],[578,1467,1420],{"className":1468},[622,775],[578,1470,1158],{"className":1471},[622,775]," (auf dem Taschenrechner oft ",[1474,1475,1476],"code",{},"SHIFT"," + ",[1474,1479,795],{},").",[560,1482,1484],{"id":1483},"beispiele","Beispiele",[565,1486,1487,1488,934,1533,1576,1577,1620,1621,1649,1650,1691],{},"Ein rechtwinkliges Dreieck hat die Katheten ",[578,1489,1491,1512],{"className":1490},[581],[578,1492,1494],{"className":1493},[585],[587,1495,1496],{"xmlns":589},[591,1497,1498,1509],{},[594,1499,1500,1503,1506],{},[692,1501,1502],{},"3",[1192,1504,1505],{}," ",[1192,1507,1508],{},"cm",[601,1510,1511],{"encoding":603},"3\\,\\text{cm}",[578,1513,1515],{"className":1514,"ariaHidden":609},[608],[578,1516,1518,1521,1524,1527],{"className":1517},[613],[578,1519],{"className":1520,"style":1140},[617],[578,1522,1502],{"className":1523},[622],[578,1525],{"className":1526,"style":832},[718],[578,1528,1530],{"className":1529},[622,1241],[578,1531,1508],{"className":1532},[622],[578,1534,1536,1555],{"className":1535},[581],[578,1537,1539],{"className":1538},[585],[587,1540,1541],{"xmlns":589},[591,1542,1543,1552],{},[594,1544,1545,1548,1550],{},[692,1546,1547],{},"4",[1192,1549,1505],{},[1192,1551,1508],{},[601,1553,1554],{"encoding":603},"4\\,\\text{cm}",[578,1556,1558],{"className":1557,"ariaHidden":609},[608],[578,1559,1561,1564,1567,1570],{"className":1560},[613],[578,1562],{"className":1563,"style":1140},[617],[578,1565,1547],{"className":1566},[622],[578,1568],{"className":1569,"style":832},[718],[578,1571,1573],{"className":1572},[622,1241],[578,1574,1508],{"className":1575},[622]," und die Hypotenuse ",[578,1578,1580,1599],{"className":1579},[581],[578,1581,1583],{"className":1582},[585],[587,1584,1585],{"xmlns":589},[591,1586,1587,1596],{},[594,1588,1589,1592,1594],{},[692,1590,1591],{},"5",[1192,1593,1505],{},[1192,1595,1508],{},[601,1597,1598],{"encoding":603},"5\\,\\text{cm}",[578,1600,1602],{"className":1601,"ariaHidden":609},[608],[578,1603,1605,1608,1611,1614],{"className":1604},[613],[578,1606],{"className":1607,"style":1140},[617],[578,1609,1591],{"className":1610},[622],[578,1612],{"className":1613,"style":832},[718],[578,1615,1617],{"className":1616},[622,1241],[578,1618,1508],{"className":1619},[622],". Für den Winkel ",[578,1622,1624,1637],{"className":1623},[581],[578,1625,1627],{"className":1626},[585],[587,1628,1629],{"xmlns":589},[591,1630,1631,1635],{},[594,1632,1633],{},[597,1634,599],{},[601,1636,604],{"encoding":603},[578,1638,1640],{"className":1639,"ariaHidden":609},[608],[578,1641,1643,1646],{"className":1642},[613],[578,1644],{"className":1645,"style":618},[617],[578,1647,599],{"className":1648,"style":624},[622,623]," gegenüber der Seite ",[578,1651,1653,1670],{"className":1652},[581],[578,1654,1656],{"className":1655},[585],[587,1657,1658],{"xmlns":589},[591,1659,1660,1668],{},[594,1661,1662,1664,1666],{},[692,1663,1502],{},[1192,1665,1505],{},[1192,1667,1508],{},[601,1669,1511],{"encoding":603},[578,1671,1673],{"className":1672,"ariaHidden":609},[608],[578,1674,1676,1679,1682,1685],{"className":1675},[613],[578,1677],{"className":1678,"style":1140},[617],[578,1680,1502],{"className":1681},[622],[578,1683],{"className":1684,"style":832},[718],[578,1686,1688],{"className":1687},[622,1241],[578,1689,1508],{"className":1690},[622]," gilt:",[578,1693,1695],{"className":1694},[1177],[578,1696,1698,1774],{"className":1697},[581],[578,1699,1701],{"className":1700},[585],[587,1702,1703],{"xmlns":589,"display":1186},[591,1704,1705,1771],{},[594,1706,1707,1709,1711,1713,1715,1721,1723,1726,1729,1732,1734,1736,1738,1752,1756,1758,1761,1764],{},[597,1708,795],{},[685,1710,798],{},[597,1712,599],{},[685,1714,687],{},[804,1716,1717,1719],{},[692,1718,1502],{},[692,1720,1591],{},[685,1722,687],{},[692,1724,1725],{},"0,6",[718,1727],{"width":1728},"1em",[685,1730,1731],{},"⇒",[718,1733],{"width":1728},[597,1735,599],{},[685,1737,687],{},[689,1739,1740,1746],{},[594,1741,1742,1744],{},[597,1743,795],{},[685,1745,798],{},[594,1747,1748,1750],{},[685,1749,1420],{},[692,1751,1158],{},[685,1753,1755],{"stretchy":1754},"false","(",[692,1757,1725],{},[685,1759,1760],{"stretchy":1754},")",[685,1762,1763],{},"≈",[689,1765,1766,1769],{},[692,1767,1768],{},"36,87",[685,1770,697],{},[601,1772,1773],{"encoding":603},"\\sin \\alpha = \\frac{3}{5} = 0{,}6\n\\quad\\Rightarrow\\quad\n\\alpha = \\sin^{-1}(0{,}6) \\approx 36{,}87^\\circ",[578,1775,1777,1801,1880,1918,1936,2005],{"className":1776,"ariaHidden":609},[608],[578,1778,1780,1783,1786,1789,1792,1795,1798],{"className":1779},[613],[578,1781],{"className":1782,"style":824},[617],[578,1784,795],{"className":1785},[828],[578,1787],{"className":1788,"style":832},[718],[578,1790,599],{"className":1791,"style":624},[622,623],[578,1793],{"className":1794,"style":719},[718],[578,1796,687],{"className":1797},[723],[578,1799],{"className":1800,"style":719},[718],[578,1802,1804,1808,1871,1874,1877],{"className":1803},[613],[578,1805],{"className":1806,"style":1807},[617],"height:2.0074em;vertical-align:-0.686em;",[578,1809,1811,1814,1868],{"className":1810},[622],[578,1812],{"className":1813},[858,859],[578,1815,1817],{"className":1816},[804],[578,1818,1820,1860],{"className":1819},[752,866],[578,1821,1823,1857],{"className":1822},[756],[578,1824,1827,1838,1846],{"className":1825,"style":1826},[760],"height:1.3214em;",[578,1828,1829,1832],{"style":1339},[578,1830],{"className":1831,"style":880},[767],[578,1833,1835],{"className":1834},[622],[578,1836,1591],{"className":1837},[622],[578,1839,1840,1843],{"style":892},[578,1841],{"className":1842,"style":880},[767],[578,1844],{"className":1845,"style":900},[899],[578,1847,1848,1851],{"style":1365},[578,1849],{"className":1850,"style":880},[767],[578,1852,1854],{"className":1853},[622],[578,1855,1502],{"className":1856},[622],[578,1858,920],{"className":1859},[919],[578,1861,1863],{"className":1862},[756],[578,1864,1866],{"className":1865,"style":1387},[760],[578,1867],{},[578,1869],{"className":1870},[933,859],[578,1872],{"className":1873,"style":719},[718],[578,1875,687],{"className":1876},[723],[578,1878],{"className":1879,"style":719},[718],[578,1881,1883,1887,1890,1898,1902,1906,1909,1912,1915],{"className":1882},[613],[578,1884],{"className":1885,"style":1886},[617],"height:0.8389em;vertical-align:-0.1944em;",[578,1888,744],{"className":1889},[622],[578,1891,1893],{"className":1892},[622],[578,1894,1897],{"className":1895},[1896],"mpunct",",",[578,1899,1901],{"className":1900},[622],"6",[578,1903],{"className":1904,"style":1905},[718],"margin-right:1em;",[578,1907],{"className":1908,"style":719},[718],[578,1910,1731],{"className":1911},[723],[578,1913],{"className":1914,"style":1905},[718],[578,1916],{"className":1917,"style":719},[718],[578,1919,1921,1924,1927,1930,1933],{"className":1920},[613],[578,1922],{"className":1923,"style":618},[617],[578,1925,599],{"className":1926,"style":624},[622,623],[578,1928],{"className":1929,"style":719},[718],[578,1931,687],{"className":1932},[723],[578,1934],{"className":1935,"style":719},[718],[578,1937,1939,1943,1978,1981,1984,1990,1993,1996,1999,2002],{"className":1938},[613],[578,1940],{"className":1941,"style":1942},[617],"height:1.1219em;vertical-align:-0.25em;",[578,1944,1946,1949],{"className":1945},[828],[578,1947,795],{"className":1948},[828],[578,1950,1952],{"className":1951},[748],[578,1953,1955],{"className":1954},[752],[578,1956,1958],{"className":1957},[756],[578,1959,1961],{"className":1960,"style":1435},[760],[578,1962,1963,1966],{"style":1456},[578,1964],{"className":1965,"style":768},[767],[578,1967,1969],{"className":1968},[772,773,774,775],[578,1970,1972,1975],{"className":1971},[622,775],[578,1973,1420],{"className":1974},[622,775],[578,1976,1158],{"className":1977},[622,775],[578,1979,1755],{"className":1980},[858],[578,1982,744],{"className":1983},[622],[578,1985,1987],{"className":1986},[622],[578,1988,1897],{"className":1989},[1896],[578,1991,1901],{"className":1992},[622],[578,1994,1760],{"className":1995},[933],[578,1997],{"className":1998,"style":719},[718],[578,2000,1763],{"className":2001},[723],[578,2003],{"className":2004,"style":719},[718],[578,2006,2008,2012,2016,2022,2026],{"className":2007},[613],[578,2009],{"className":2010,"style":2011},[617],"height:0.9186em;vertical-align:-0.1944em;",[578,2013,2015],{"className":2014},[622],"36",[578,2017,2019],{"className":2018},[622],[578,2020,1897],{"className":2021},[1896],[578,2023,2025],{"className":2024},[622],"8",[578,2027,2029,2033],{"className":2028},[622],[578,2030,2032],{"className":2031},[622],"7",[578,2034,2036],{"className":2035},[748],[578,2037,2039],{"className":2038},[752],[578,2040,2042],{"className":2041},[756],[578,2043,2046],{"className":2044,"style":2045},[760],"height:0.7241em;",[578,2047,2049,2052],{"style":2048},"top:-3.113em;margin-right:0.05em;",[578,2050],{"className":2051,"style":768},[767],[578,2053,2055],{"className":2054},[772,773,774,775],[578,2056,697],{"className":2057},[779,775],[565,2059,2060,2061,2104,2105,2190],{},"Die Hypotenuse ist ",[578,2062,2064,2083],{"className":2063},[581],[578,2065,2067],{"className":2066},[585],[587,2068,2069],{"xmlns":589},[591,2070,2071,2080],{},[594,2072,2073,2076,2078],{},[692,2074,2075],{},"10",[1192,2077,1505],{},[1192,2079,1508],{},[601,2081,2082],{"encoding":603},"10\\,\\text{cm}",[578,2084,2086],{"className":2085,"ariaHidden":609},[608],[578,2087,2089,2092,2095,2098],{"className":2088},[613],[578,2090],{"className":2091,"style":1140},[617],[578,2093,2075],{"className":2094},[622],[578,2096],{"className":2097,"style":832},[718],[578,2099,2101],{"className":2100},[622,1241],[578,2102,1508],{"className":2103},[622]," lang, der Winkel ",[578,2106,2108,2131],{"className":2107},[581],[578,2109,2111],{"className":2110},[585],[587,2112,2113],{"xmlns":589},[591,2114,2115,2128],{},[594,2116,2117,2119,2121],{},[597,2118,599],{},[685,2120,687],{},[689,2122,2123,2126],{},[692,2124,2125],{},"30",[685,2127,697],{},[601,2129,2130],{"encoding":603},"\\alpha = 30^\\circ",[578,2132,2134,2152],{"className":2133,"ariaHidden":609},[608],[578,2135,2137,2140,2143,2146,2149],{"className":2136},[613],[578,2138],{"className":2139,"style":618},[617],[578,2141,599],{"className":2142,"style":624},[622,623],[578,2144],{"className":2145,"style":719},[718],[578,2147,687],{"className":2148},[723],[578,2150],{"className":2151,"style":719},[718],[578,2153,2155,2158,2161],{"className":2154},[613],[578,2156],{"className":2157,"style":733},[617],[578,2159,1502],{"className":2160},[622],[578,2162,2164,2167],{"className":2163},[622],[578,2165,744],{"className":2166},[622],[578,2168,2170],{"className":2169},[748],[578,2171,2173],{"className":2172},[752],[578,2174,2176],{"className":2175},[756],[578,2177,2179],{"className":2178,"style":733},[760],[578,2180,2181,2184],{"style":763},[578,2182],{"className":2183,"style":768},[767],[578,2185,2187],{"className":2186},[772,773,774,775],[578,2188,697],{"className":2189},[779,775],". Gesucht ist die Gegenkathete:",[578,2192,2194],{"className":2193},[1177],[578,2195,2197,2252],{"className":2196},[581],[578,2198,2200],{"className":2199},[585],[587,2201,2202],{"xmlns":589,"display":1186},[591,2203,2204,2249],{},[594,2205,2206,2208,2210,2212,2214,2216,2218,2220,2222,2228,2230,2232,2234,2236,2238,2241,2243,2245,2247],{},[1192,2207,628],{},[685,2209,687],{},[692,2211,2075],{},[1192,2213,1505],{},[1192,2215,1508],{},[685,2217,1200],{},[597,2219,795],{},[685,2221,798],{},[689,2223,2224,2226],{},[692,2225,2125],{},[685,2227,697],{},[685,2229,687],{},[692,2231,2075],{},[1192,2233,1505],{},[1192,2235,1508],{},[685,2237,1200],{},[692,2239,2240],{},"0,5",[685,2242,687],{},[692,2244,1591],{},[1192,2246,1505],{},[1192,2248,1508],{},[601,2250,2251],{"encoding":603},"\\text{Gegenkathete} = 10\\,\\text{cm} \\cdot \\sin 30^\\circ = 10\\,\\text{cm} \\cdot 0{,}5 = 5\\,\\text{cm}",[578,2253,2255,2276,2303,2356,2383,2410],{"className":2254,"ariaHidden":609},[608],[578,2256,2258,2261,2267,2270,2273],{"className":2257},[613],[578,2259],{"className":2260,"style":975},[617],[578,2262,2264],{"className":2263},[622,1241],[578,2265,628],{"className":2266},[622],[578,2268],{"className":2269,"style":719},[718],[578,2271,687],{"className":2272},[723],[578,2274],{"className":2275,"style":719},[718],[578,2277,2279,2282,2285,2288,2294,2297,2300],{"className":2278},[613],[578,2280],{"className":2281,"style":1140},[617],[578,2283,2075],{"className":2284},[622],[578,2286],{"className":2287,"style":832},[718],[578,2289,2291],{"className":2290},[622,1241],[578,2292,1508],{"className":2293},[622],[578,2295],{"className":2296,"style":1270},[718],[578,2298,1200],{"className":2299},[779],[578,2301],{"className":2302,"style":1270},[718],[578,2304,2306,2309,2312,2315,2318,2347,2350,2353],{"className":2305},[613],[578,2307],{"className":2308,"style":2045},[617],[578,2310,795],{"className":2311},[828],[578,2313],{"className":2314,"style":832},[718],[578,2316,1502],{"className":2317},[622],[578,2319,2321,2324],{"className":2320},[622],[578,2322,744],{"className":2323},[622],[578,2325,2327],{"className":2326},[748],[578,2328,2330],{"className":2329},[752],[578,2331,2333],{"className":2332},[756],[578,2334,2336],{"className":2335,"style":2045},[760],[578,2337,2338,2341],{"style":2048},[578,2339],{"className":2340,"style":768},[767],[578,2342,2344],{"className":2343},[772,773,774,775],[578,2345,697],{"className":2346},[779,775],[578,2348],{"className":2349,"style":719},[718],[578,2351,687],{"className":2352},[723],[578,2354],{"className":2355,"style":719},[718],[578,2357,2359,2362,2365,2368,2374,2377,2380],{"className":2358},[613],[578,2360],{"className":2361,"style":1140},[617],[578,2363,2075],{"className":2364},[622],[578,2366],{"className":2367,"style":832},[718],[578,2369,2371],{"className":2370},[622,1241],[578,2372,1508],{"className":2373},[622],[578,2375],{"className":2376,"style":1270},[718],[578,2378,1200],{"className":2379},[779],[578,2381],{"className":2382,"style":1270},[718],[578,2384,2386,2389,2392,2398,2401,2404,2407],{"className":2385},[613],[578,2387],{"className":2388,"style":1886},[617],[578,2390,744],{"className":2391},[622],[578,2393,2395],{"className":2394},[622],[578,2396,1897],{"className":2397},[1896],[578,2399,1591],{"className":2400},[622],[578,2402],{"className":2403,"style":719},[718],[578,2405,687],{"className":2406},[723],[578,2408],{"className":2409,"style":719},[718],[578,2411,2413,2416,2419,2422],{"className":2412},[613],[578,2414],{"className":2415,"style":1140},[617],[578,2417,1591],{"className":2418},[622],[578,2420],{"className":2421,"style":832},[718],[578,2423,2425],{"className":2424},[622,1241],[578,2426,1508],{"className":2427},[622],[565,2429,2430,2431,2474,2475,2538],{},"Eine ",[578,2432,2434,2453],{"className":2433},[581],[578,2435,2437],{"className":2436},[585],[587,2438,2439],{"xmlns":589},[591,2440,2441,2450],{},[594,2442,2443,2445,2447],{},[692,2444,2025],{},[1192,2446,1505],{},[1192,2448,2449],{},"m",[601,2451,2452],{"encoding":603},"8\\,\\text{m}",[578,2454,2456],{"className":2455,"ariaHidden":609},[608],[578,2457,2459,2462,2465,2468],{"className":2458},[613],[578,2460],{"className":2461,"style":1140},[617],[578,2463,2025],{"className":2464},[622],[578,2466],{"className":2467,"style":832},[718],[578,2469,2471],{"className":2470},[622,1241],[578,2472,2449],{"className":2473},[622]," lange Rampe ist um ",[578,2476,2478,2497],{"className":2477},[581],[578,2479,2481],{"className":2480},[585],[587,2482,2483],{"xmlns":589},[591,2484,2485,2494],{},[594,2486,2487],{},[689,2488,2489,2492],{},[692,2490,2491],{},"40",[685,2493,697],{},[601,2495,2496],{"encoding":603},"40^\\circ",[578,2498,2500],{"className":2499,"ariaHidden":609},[608],[578,2501,2503,2506,2509],{"className":2502},[613],[578,2504],{"className":2505,"style":733},[617],[578,2507,1547],{"className":2508},[622],[578,2510,2512,2515],{"className":2511},[622],[578,2513,744],{"className":2514},[622],[578,2516,2518],{"className":2517},[748],[578,2519,2521],{"className":2520},[752],[578,2522,2524],{"className":2523},[756],[578,2525,2527],{"className":2526,"style":733},[760],[578,2528,2529,2532],{"style":763},[578,2530],{"className":2531,"style":768},[767],[578,2533,2535],{"className":2534},[772,773,774,775],[578,2536,697],{"className":2537},[779,775]," gegen den Boden geneigt. Wie hoch führt sie? Die Rampe ist die Hypotenuse, die Höhe die Gegenkathete:",[578,2540,2542],{"className":2541},[1177],[578,2543,2545,2589],{"className":2544},[581],[578,2546,2548],{"className":2547},[585],[587,2549,2550],{"xmlns":589,"display":1186},[591,2551,2552,2586],{},[594,2553,2554,2557,2559,2561,2563,2565,2567,2569,2571,2577,2579,2582,2584],{},[597,2555,2556],{},"h",[685,2558,687],{},[692,2560,2025],{},[1192,2562,1505],{},[1192,2564,2449],{},[685,2566,1200],{},[597,2568,795],{},[685,2570,798],{},[689,2572,2573,2575],{},[692,2574,2491],{},[685,2576,697],{},[685,2578,1763],{},[692,2580,2581],{},"5,14",[1192,2583,1505],{},[1192,2585,2449],{},[601,2587,2588],{"encoding":603},"h = 8\\,\\text{m} \\cdot \\sin 40^\\circ \\approx 5{,}14\\,\\text{m}",[578,2590,2592,2611,2638,2691],{"className":2591,"ariaHidden":609},[608],[578,2593,2595,2599,2602,2605,2608],{"className":2594},[613],[578,2596],{"className":2597,"style":2598},[617],"height:0.6944em;",[578,2600,2556],{"className":2601},[622,623],[578,2603],{"className":2604,"style":719},[718],[578,2606,687],{"className":2607},[723],[578,2609],{"className":2610,"style":719},[718],[578,2612,2614,2617,2620,2623,2629,2632,2635],{"className":2613},[613],[578,2615],{"className":2616,"style":1140},[617],[578,2618,2025],{"className":2619},[622],[578,2621],{"className":2622,"style":832},[718],[578,2624,2626],{"className":2625},[622,1241],[578,2627,2449],{"className":2628},[622],[578,2630],{"className":2631,"style":1270},[718],[578,2633,1200],{"className":2634},[779],[578,2636],{"className":2637,"style":1270},[718],[578,2639,2641,2644,2647,2650,2653,2682,2685,2688],{"className":2640},[613],[578,2642],{"className":2643,"style":2045},[617],[578,2645,795],{"className":2646},[828],[578,2648],{"className":2649,"style":832},[718],[578,2651,1547],{"className":2652},[622],[578,2654,2656,2659],{"className":2655},[622],[578,2657,744],{"className":2658},[622],[578,2660,2662],{"className":2661},[748],[578,2663,2665],{"className":2664},[752],[578,2666,2668],{"className":2667},[756],[578,2669,2671],{"className":2670,"style":2045},[760],[578,2672,2673,2676],{"style":2048},[578,2674],{"className":2675,"style":768},[767],[578,2677,2679],{"className":2678},[772,773,774,775],[578,2680,697],{"className":2681},[779,775],[578,2683],{"className":2684,"style":719},[718],[578,2686,1763],{"className":2687},[723],[578,2689],{"className":2690,"style":719},[718],[578,2692,2694,2697,2700,2706,2710,2713],{"className":2693},[613],[578,2695],{"className":2696,"style":1886},[617],[578,2698,1591],{"className":2699},[622],[578,2701,2703],{"className":2702},[622],[578,2704,1897],{"className":2705},[1896],[578,2707,2709],{"className":2708},[622],"14",[578,2711],{"className":2712,"style":832},[718],[578,2714,2716],{"className":2715},[622,1241],[578,2717,2449],{"className":2718},[622],[560,2720,2722],{"id":2721},"typische-fehler","Typische Fehler",[2724,2725,2726,2759,2886,3322],"ul",{},[2727,2728,2729,2730,2758],"li",{},"Die falsche Kathete als Gegenkathete nehmen. Die Gegenkathete berührt den Winkel ",[578,2731,2733,2746],{"className":2732},[581],[578,2734,2736],{"className":2735},[585],[587,2737,2738],{"xmlns":589},[591,2739,2740,2744],{},[594,2741,2742],{},[597,2743,599],{},[601,2745,604],{"encoding":603},[578,2747,2749],{"className":2748,"ariaHidden":609},[608],[578,2750,2752,2755],{"className":2751},[613],[578,2753],{"className":2754,"style":618},[617],[578,2756,599],{"className":2757,"style":624},[622,623]," nicht, sie liegt ihm gegenüber.",[2727,2760,2761,2762,2765,2766,2769,2770,2847,2848,1071],{},"Den Taschenrechner im Bogenmaß (",[1474,2763,2764],{},"RAD",") statt im Gradmaß (",[1474,2767,2768],{},"DEG",") rechnen lassen: Dann ist ",[578,2771,2773,2798],{"className":2772},[581],[578,2774,2776],{"className":2775},[585],[587,2777,2778],{"xmlns":589},[591,2779,2780,2795],{},[594,2781,2782,2784,2786,2788,2790,2792],{},[597,2783,795],{},[685,2785,798],{},[692,2787,2125],{},[685,2789,1763],{},[685,2791,1420],{},[692,2793,2794],{},"0,99",[601,2796,2797],{"encoding":603},"\\sin 30 \\approx -0{,}99",[578,2799,2801,2825],{"className":2800,"ariaHidden":609},[608],[578,2802,2804,2807,2810,2813,2816,2819,2822],{"className":2803},[613],[578,2805],{"className":2806,"style":824},[617],[578,2808,795],{"className":2809},[828],[578,2811],{"className":2812,"style":832},[718],[578,2814,2125],{"className":2815},[622],[578,2817],{"className":2818,"style":719},[718],[578,2820,1763],{"className":2821},[723],[578,2823],{"className":2824,"style":719},[718],[578,2826,2828,2831,2834,2837,2843],{"className":2827},[613],[578,2829],{"className":2830,"style":1886},[617],[578,2832,1420],{"className":2833},[622],[578,2835,744],{"className":2836},[622],[578,2838,2840],{"className":2839},[622],[578,2841,1897],{"className":2842},[1896],[578,2844,2846],{"className":2845},[622],"99"," statt ",[578,2849,2851,2865],{"className":2850},[581],[578,2852,2854],{"className":2853},[585],[587,2855,2856],{"xmlns":589},[591,2857,2858,2862],{},[594,2859,2860],{},[692,2861,2240],{},[601,2863,2864],{"encoding":603},"0{,}5",[578,2866,2868],{"className":2867,"ariaHidden":609},[608],[578,2869,2871,2874,2877,2883],{"className":2870},[613],[578,2872],{"className":2873,"style":1886},[617],[578,2875,744],{"className":2876},[622],[578,2878,2880],{"className":2879},[622],[578,2881,1897],{"className":2882},[1896],[578,2884,1591],{"className":2885},[622],[2727,2887,2888,2960,2961,3075,3076,3173,3174,3212,3213,1071],{},[578,2889,2891,2916],{"className":2890},[581],[578,2892,2894],{"className":2893},[585],[587,2895,2896],{"xmlns":589},[591,2897,2898,2914],{},[594,2899,2900],{},[689,2901,2902,2908],{},[594,2903,2904,2906],{},[597,2905,795],{},[685,2907,798],{},[594,2909,2910,2912],{},[685,2911,1420],{},[692,2913,1158],{},[601,2915,1425],{"encoding":603},[578,2917,2919],{"className":2918,"ariaHidden":609},[608],[578,2920,2922,2925],{"className":2921},[613],[578,2923],{"className":2924,"style":1435},[617],[578,2926,2928,2931],{"className":2927},[828],[578,2929,795],{"className":2930},[828],[578,2932,2934],{"className":2933},[748],[578,2935,2937],{"className":2936},[752],[578,2938,2940],{"className":2939},[756],[578,2941,2943],{"className":2942,"style":1435},[760],[578,2944,2945,2948],{"style":1456},[578,2946],{"className":2947,"style":768},[767],[578,2949,2951],{"className":2950},[772,773,774,775],[578,2952,2954,2957],{"className":2953},[622,775],[578,2955,1420],{"className":2956},[622,775],[578,2958,1158],{"className":2959},[622,775]," mit 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verwechseln. ",[578,3077,3079,3111],{"className":3078},[581],[578,3080,3082],{"className":3081},[585],[587,3083,3084],{"xmlns":589},[591,3085,3086,3108],{},[594,3087,3088,3102,3104,3106],{},[689,3089,3090,3096],{},[594,3091,3092,3094],{},[597,3093,795],{},[685,3095,798],{},[594,3097,3098,3100],{},[685,3099,1420],{},[692,3101,1158],{},[685,3103,1755],{"stretchy":1754},[692,3105,1725],{},[685,3107,1760],{"stretchy":1754},[601,3109,3110],{"encoding":603},"\\sin^{-1}(0{,}6)",[578,3112,3114],{"className":3113,"ariaHidden":609},[608],[578,3115,3117,3120,3155,3158,3161,3167,3170],{"className":3116},[613],[578,3118],{"className":3119,"style":1942},[617],[578,3121,3123,3126],{"className":3122},[828],[578,3124,795],{"className":3125},[828],[578,3127,3129],{"className":3128},[748],[578,3130,3132],{"className":3131},[752],[578,3133,3135],{"className":3134},[756],[578,3136,3138],{"className":3137,"style":1435},[760],[578,3139,3140,3143],{"style":1456},[578,3141],{"className":3142,"style":768},[767],[578,3144,3146],{"className":3145},[772,773,774,775],[578,3147,3149,3152],{"className":3148},[622,775],[578,3150,1420],{"className":3151},[622,775],[578,3153,1158],{"className":3154},[622,775],[578,3156,1755],{"className":3157},[858],[578,3159,744],{"className":3160},[622],[578,3162,3164],{"className":3163},[622],[578,3165,1897],{"className":3166},[1896],[578,3168,1901],{"className":3169},[622],[578,3171,1760],{"className":3172},[933]," ist der Winkel, dessen Sinus ",[578,3175,3177,3191],{"className":3176},[581],[578,3178,3180],{"className":3179},[585],[587,3181,3182],{"xmlns":589},[591,3183,3184,3188],{},[594,3185,3186],{},[692,3187,1725],{},[601,3189,3190],{"encoding":603},"0{,}6",[578,3192,3194],{"className":3193,"ariaHidden":609},[608],[578,3195,3197,3200,3203,3209],{"className":3196},[613],[578,3198],{"className":3199,"style":1886},[617],[578,3201,744],{"className":3202},[622],[578,3204,3206],{"className":3205},[622],[578,3207,1897],{"className":3208},[1896],[578,3210,1901],{"className":3211},[622]," ist, nicht ",[578,3214,3216,3234],{"className":3215},[581],[578,3217,3219],{"className":3218},[585],[587,3220,3221],{"xmlns":589},[591,3222,3223,3231],{},[594,3224,3225],{},[804,3226,3227,3229],{},[692,3228,1158],{},[692,3230,1725],{},[601,3232,3233],{"encoding":603},"\\frac{1}{0{,}6}",[578,3235,3237],{"className":3236,"ariaHidden":609},[608],[578,3238,3240,3244],{"className":3239},[613],[578,3241],{"className":3242,"style":3243},[617],"height:1.3262em;vertical-align:-0.4811em;",[578,3245,3247,3250,3319],{"className":3246},[622],[578,3248],{"className":3249},[858,859],[578,3251,3253],{"className":3252},[804],[578,3254,3256,3310],{"className":3255},[752,866],[578,3257,3259,3307],{"className":3258},[756],[578,3260,3262,3285,3293],{"className":3261,"style":3012},[760],[578,3263,3264,3267],{"style":876},[578,3265],{"className":3266,"style":880},[767],[578,3268,3270],{"className":3269},[772,773,774,775],[578,3271,3273,3276,3282],{"className":3272},[622,775],[578,3274,744],{"className":3275},[622,775],[578,3277,3279],{"className":3278},[622,775],[578,3280,1897],{"className":3281},[1896,775],[578,3283,1901],{"className":3284},[622,775],[578,3286,3287,3290],{"style":892},[578,3288],{"className":3289,"style":880},[767],[578,3291],{"className":3292,"style":900},[899],[578,3294,3295,3298],{"style":903},[578,3296],{"className":3297,"style":880},[767],[578,3299,3301],{"className":3300},[772,773,774,775],[578,3302,3304],{"className":3303},[622,775],[578,3305,1158],{"className":3306},[622,775],[578,3308,920],{"className":3309},[919],[578,3311,3313],{"className":3312},[756],[578,3314,3317],{"className":3315,"style":3316},[760],"height:0.4811em;",[578,3318],{},[578,3320],{"className":3321},[933,859],[2727,3323,3324],{},"Die Formel im nicht rechtwinkligen Dreieck verwenden. Dort helfen Sinussatz oder Kosinussatz.",{"title":3326,"searchDepth":3327,"depth":3327,"links":3328},"",2,[3329,3330,3331],{"id":562,"depth":3327,"text":563},{"id":1483,"depth":3327,"text":1484},{"id":2721,"depth":3327,"text":2722},[3333,3336,3339,3342,3344,3347],{"lhs":3334,"rhs":3335},"sin(atan(a\u002Fb))","a\u002Fsqrt(a^2 + b^2)",{"lhs":3337,"rhs":3338},"3\u002F5","0.6",{"lhs":3340,"rhs":3341},"round(asin(3\u002F5) * 180\u002Fpi, 2)","36.87",{"lhs":3343,"rhs":1591},"10 * sin(30*pi\u002F180)",{"lhs":3345,"rhs":3346},"round(8 * sin(40*pi\u002F180), 2)","5.14",{"lhs":3348,"rhs":3349},"round(sin(30), 2)","-0.99","\\text{rechtwinkliges Dreieck},\\ 0^\\circ \u003C \\alpha \u003C 90^\\circ","\u003Cspan class=\"katex\">rechtwinkliges\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Dreieck\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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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>α\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0^\\circ < \\alpha < 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:0.7132em;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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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":3355,"x":3356,"y":3359,"unit":3362,"items":3363},"Rechtwinkliges Dreieck mit dem Winkel α, hervorgehoben sind Gegenkathete und Hypotenuse",[3357,3358],-0.6,7,[3360,3361],-0.8,3.5,40,[3364,3375,3379,3382,3387,3392,3397,3401],{"type":3365,"points":3366,"fill":3373,"style":3374},"polygon",[3367,3369,3371],[3368,3368],0,[3370,3368],4,[3370,3372],3,true,"muted",{"type":3376,"from":3377,"to":3378},"segment",[3370,3368],[3370,3372],{"type":3376,"from":3380,"to":3381},[3368,3368],[3370,3372],{"type":3383,"at":3384,"from":3385,"to":3386},"rightAngle",[3370,3368],[3368,3368],[3370,3372],{"type":3388,"at":3389,"from":3390,"to":3391,"label":599},"angle",[3368,3368],[3370,3368],[3370,3372],{"type":3393,"at":3394,"text":3396,"upright":3373},"label",[3327,3395],-0.45,"Ankathete",{"type":3393,"at":3398,"text":628,"upright":3373},[3399,3400],5.55,1.5,{"type":3393,"at":3402,"text":661,"upright":3373},[3403,3404],1.3,2.3,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 304 172\" width=\"304\" height=\"172\" role=\"img\" aria-label=\"Rechtwinkliges Dreieck mit dem Winkel α, hervorgehoben sind Gegenkathete und Hypotenuse\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-sine-right-triangle-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-sine-right-triangle-clip\">\u003Crect x=\"0\" y=\"0\" width=\"304\" height=\"172\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,140 184,140 184,20\" class=\"fig-muted fig-fill\"\u002F>\u003Cline x1=\"184\" y1=\"140\" x2=\"184\" y2=\"20\" class=\"fig-main\"\u002F>\u003Cline x1=\"24\" y1=\"140\" x2=\"184\" y2=\"20\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 172 140 L 172 128 L 184 128\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"178\" cy=\"134\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Cpath d=\"M 24 140 L 46 140 A 22 22 0 0 0 41.6 126.8 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"56.26\" y=\"129.25\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Ctext x=\"104\" y=\"158\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">Ankathete\u003C\u002Ftext>\u003Ctext x=\"246\" y=\"80\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">Gegenkathete\u003C\u002Ftext>\u003Ctext x=\"76\" y=\"48\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">Hypotenuse\u003C\u002Ftext>\u003C\u002Fsvg>","sine-right-triangle","\\sin \\alpha = \\frac{\\text{Gegenkathete}}{\\text{Hypotenuse}}","\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>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmtext>Gegenkathete\u003C\u002Fmtext>\u003Cmtext>Hypotenuse\u003C\u002Fmtext>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sin \\alpha = \\frac{\\text{Gegenkathete}}{\\text{Hypotenuse}}\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:0.6679em;\">\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:0.0037em;\">α\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:2.2519em;vertical-align:-0.8804em;\">\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:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Hypotenuse\u003C\u002Fspan>\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 text\">\u003Cspan class=\"mord\">Gegenkathete\u003C\u002Fspan>\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:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck",[],[3414,3415,3416,3417],"cosine-right-triangle","tangent-right-triangle","pythagorean-theorem","law-of-sines",{"title":548,"description":3326},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck","Im rechtwinkligen Dreieck ist der Sinus eines spitzen Winkels das Verhältnis von Gegenkathete zu Hypotenuse.",[3422,3423,3424,3425,3426],"sinus","rechtwinkliges dreieck","gegenkathete","hypotenuse","winkel",[3428,3431,3435],{"symbol":604,"meaning":3429,"symbolHtml":3430},"einer der beiden spitzen Winkel des Dreiecks (nicht der rechte Winkel)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha\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\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3432,"meaning":3433,"symbolHtml":3434},"\\text{Gegenkathete}","Kathete, die dem Winkel α gegenüberliegt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmtext>Gegenkathete\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\text{Gegenkathete}\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 text\">\u003Cspan class=\"mord\">Gegenkathete\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3436,"meaning":3437,"symbolHtml":3438},"\\text{Hypotenuse}","längste Seite, sie liegt dem rechten Winkel gegenüber","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmtext>Hypotenuse\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\text{Hypotenuse}\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Hypotenuse\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lxUdGO_ia7PrkYLBWyWh4F4Xhvm1579lattnFIJUt_I",[3441,3444,3447,3450],{"stem":3442,"title":3443,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des Pythagoras",{"stem":3445,"title":3446,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fkosinus-im-rechtwinkligen-dreieck","Kosinus im rechtwinkligen Dreieck",{"stem":3448,"title":3449,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinussatz","Sinussatz",{"stem":3451,"title":3452,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftangens-im-rechtwinkligen-dreieck","Tangens im rechtwinkligen Dreieck",1793824262941]