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90^\\circ",[568,1163,1165,1183],{"className":1164,"ariaHidden":598},[597],[568,1166,1168,1171,1174,1177,1180],{"className":1167},[602],[568,1169],{"className":1170,"style":972},[606],[568,1172,659],{"className":1173,"style":675},[611,612],[568,1175],{"className":1176,"style":842},[764],[568,1178,1151],{"className":1179},[846],[568,1181],{"className":1182,"style":842},[764],[568,1184,1186,1189,1193],{"className":1185},[602],[568,1187],{"className":1188,"style":891},[606],[568,1190,1192],{"className":1191},[611],"9",[568,1194,1196,1199],{"className":1195},[611],[568,1197,874],{"className":1198},[611],[568,1200,1202],{"className":1201},[878],[568,1203,1205],{"className":1204},[882],[568,1206,1208],{"className":1207},[886],[568,1209,1211],{"className":1210,"style":891},[890],[568,1212,1213,1216],{"style":894},[568,1214],{"className":1215,"style":899},[898],[568,1217,1219],{"className":1218},[903,904,905,906],[568,1220,809],{"className":1221},[910,906],", sonst keine.",[939,1224,1225,1276,1277,1360,1361],{},[568,1226,1228,1246],{"className":1227},[571],[568,1229,1231],{"className":1230},[575],[577,1232,1233],{"xmlns":579},[581,1234,1235,1243],{},[584,1236,1237,1239,1241],{},[587,1238,589],{},[738,1240,1151],{},[587,1242,628],{},[591,1244,1245],{"encoding":593},"a \u003C b",[568,1247,1249,1267],{"className":1248,"ariaHidden":598},[597],[568,1250,1252,1255,1258,1261,1264],{"className":1251},[602],[568,1253],{"className":1254,"style":972},[606],[568,1256,589],{"className":1257},[611,612],[568,1259],{"className":1260,"style":842},[764],[568,1262,1151],{"className":1263},[846],[568,1265],{"className":1266,"style":842},[764],[568,1268,1270,1273],{"className":1269},[602],[568,1271],{"className":1272,"style":640},[606],[568,1274,628],{"className":1275},[611,612]," und ",[568,1278,1280,1301],{"className":1279},[571],[568,1281,1283],{"className":1282},[575],[577,1284,1285],{"xmlns":579},[581,1286,1287,1299],{},[584,1288,1289,1291,1293],{},[587,1290,659],{},[738,1292,1151],{},[801,1294,1295,1297],{},[804,1296,1156],{},[738,1298,809],{},[591,1300,1161],{"encoding":593},[568,1302,1304,1322],{"className":1303,"ariaHidden":598},[597],[568,1305,1307,1310,1313,1316,1319],{"className":1306},[602],[568,1308],{"className":1309,"style":972},[606],[568,1311,659],{"className":1312,"style":675},[611,612],[568,1314],{"className":1315,"style":842},[764],[568,1317,1151],{"className":1318},[846],[568,1320],{"className":1321,"style":842},[764],[568,1323,1325,1328,1331],{"className":1324},[602],[568,1326],{"className":1327,"style":891},[606],[568,1329,1192],{"className":1330},[611],[568,1332,1334,1337],{"className":1333},[611],[568,1335,874],{"className":1336},[611],[568,1338,1340],{"className":1339},[878],[568,1341,1343],{"className":1342},[882],[568,1344,1346],{"className":1345},[886],[568,1347,1349],{"className":1348,"style":891},[890],[568,1350,1351,1354],{"style":894},[568,1352],{"className":1353,"style":899},[898],[568,1355,1357],{"className":1356},[903,904,905,906],[568,1358,809],{"className":1359},[910,906],":\n",[936,1362,1363,1500,1656],{},[939,1364,1365,1435,1436,1499],{},[568,1366,1368,1392],{"className":1367},[571],[568,1369,1371],{"className":1370},[575],[577,1372,1373],{"xmlns":579},[581,1374,1375,1389],{},[584,1376,1377,1379,1381,1383,1385,1387],{},[587,1378,628],{},[587,1380,736],{},[738,1382,740],{},[587,1384,659],{},[738,1386,957],{},[587,1388,589],{},[591,1390,1391],{"encoding":593},"b \\sin \\alpha > a",[568,1393,1395,1426],{"className":1394,"ariaHidden":598},[597],[568,1396,1398,1402,1405,1408,1411,1414,1417,1420,1423],{"className":1397},[602],[568,1399],{"className":1400,"style":1401},[606],"height:0.7335em;vertical-align:-0.0391em;",[568,1403,628],{"className":1404},[611,612],[568,1406],{"className":1407,"style":765},[764],[568,1409,736],{"className":1410},[760],[568,1412],{"className":1413,"style":765},[764],[568,1415,659],{"className":1416,"style":675},[611,612],[568,1418],{"className":1419,"style":842},[764],[568,1421,957],{"className":1422},[846],[568,1424],{"className":1425,"style":842},[764],[568,1427,1429,1432],{"className":1428},[602],[568,1430],{"className":1431,"style":607},[606],[568,1433,589],{"className":1434},[611,612],": keine Lösung, denn ",[568,1437,1439,1462],{"className":1438},[571],[568,1440,1442],{"className":1441},[575],[577,1443,1444],{"xmlns":579},[581,1445,1446,1459],{},[584,1447,1448,1450,1452,1454,1456],{},[587,1449,736],{},[738,1451,740],{},[587,1453,743],{},[738,1455,957],{},[804,1457,1458],{},"1",[591,1460,1461],{"encoding":593},"\\sin \\beta > 1",[568,1463,1465,1489],{"className":1464,"ariaHidden":598},[597],[568,1466,1468,1471,1474,1477,1480,1483,1486],{"className":1467},[602],[568,1469],{"className":1470,"style":756},[606],[568,1472,736],{"className":1473},[760],[568,1475],{"className":1476,"style":765},[764],[568,1478,743],{"className":1479,"style":769},[611,612],[568,1481],{"className":1482,"style":842},[764],[568,1484,957],{"className":1485},[846],[568,1487],{"className":1488,"style":842},[764],[568,1490,1492,1496],{"className":1491},[602],[568,1493],{"className":1494,"style":1495},[606],"height:0.6444em;",[568,1497,1458],{"className":1498},[611],".",[939,1501,1502,1571,1572,1499],{},[568,1503,1505,1529],{"className":1504},[571],[568,1506,1508],{"className":1507},[575],[577,1509,1510],{"xmlns":579},[581,1511,1512,1526],{},[584,1513,1514,1516,1518,1520,1522,1524],{},[587,1515,628],{},[587,1517,736],{},[738,1519,740],{},[587,1521,659],{},[738,1523,791],{},[587,1525,589],{},[591,1527,1528],{"encoding":593},"b \\sin \\alpha = a",[568,1530,1532,1562],{"className":1531,"ariaHidden":598},[597],[568,1533,1535,1538,1541,1544,1547,1550,1553,1556,1559],{"className":1534},[602],[568,1536],{"className":1537,"style":640},[606],[568,1539,628],{"className":1540},[611,612],[568,1542],{"className":1543,"style":765},[764],[568,1545,736],{"className":1546},[760],[568,1548],{"className":1549,"style":765},[764],[568,1551,659],{"className":1552,"style":675},[611,612],[568,1554],{"className":1555,"style":842},[764],[568,1557,791],{"className":1558},[846],[568,1560],{"className":1561,"style":842},[764],[568,1563,1565,1568],{"className":1564},[602],[568,1566],{"className":1567,"style":607},[606],[568,1569,589],{"className":1570},[611,612],": genau eine Lösung mit ",[568,1573,1575,1597],{"className":1574},[571],[568,1576,1578],{"className":1577},[575],[577,1579,1580],{"xmlns":579},[581,1581,1582,1594],{},[584,1583,1584,1586,1588],{},[587,1585,743],{},[738,1587,791],{},[801,1589,1590,1592],{},[804,1591,1156],{},[738,1593,809],{},[591,1595,1596],{"encoding":593},"\\beta = 90^\\circ",[568,1598,1600,1618],{"className":1599,"ariaHidden":598},[597],[568,1601,1603,1606,1609,1612,1615],{"className":1602},[602],[568,1604],{"className":1605,"style":756},[606],[568,1607,743],{"className":1608,"style":769},[611,612],[568,1610],{"className":1611,"style":842},[764],[568,1613,791],{"className":1614},[846],[568,1616],{"className":1617,"style":842},[764],[568,1619,1621,1624,1627],{"className":1620},[602],[568,1622],{"className":1623,"style":891},[606],[568,1625,1192],{"className":1626},[611],[568,1628,1630,1633],{"className":1629},[611],[568,1631,874],{"className":1632},[611],[568,1634,1636],{"className":1635},[878],[568,1637,1639],{"className":1638},[882],[568,1640,1642],{"className":1641},[886],[568,1643,1645],{"className":1644,"style":891},[890],[568,1646,1647,1650],{"style":894},[568,1648],{"className":1649,"style":899},[898],[568,1651,1653],{"className":1652},[903,904,905,906],[568,1654,809],{"className":1655},[910,906],[939,1657,1658,1727,1728,613,1731,1276,1808,1499],{},[568,1659,1661,1685],{"className":1660},[571],[568,1662,1664],{"className":1663},[575],[577,1665,1666],{"xmlns":579},[581,1667,1668,1682],{},[584,1669,1670,1672,1674,1676,1678,1680],{},[587,1671,628],{},[587,1673,736],{},[738,1675,740],{},[587,1677,659],{},[738,1679,1151],{},[587,1681,589],{},[591,1683,1684],{"encoding":593},"b \\sin \\alpha \u003C a",[568,1686,1688,1718],{"className":1687,"ariaHidden":598},[597],[568,1689,1691,1694,1697,1700,1703,1706,1709,1712,1715],{"className":1690},[602],[568,1692],{"className":1693,"style":1401},[606],[568,1695,628],{"className":1696},[611,612],[568,1698],{"className":1699,"style":765},[764],[568,1701,736],{"className":1702},[760],[568,1704],{"className":1705,"style":765},[764],[568,1707,659],{"className":1708,"style":675},[611,612],[568,1710],{"className":1711,"style":842},[764],[568,1713,1151],{"className":1714},[846],[568,1716],{"className":1717,"style":842},[764],[568,1719,1721,1724],{"className":1720},[602],[568,1722],{"className":1723,"style":607},[606],[568,1725,589],{"className":1726},[611,612],": ",[678,1729,1730],{},"zwei Lösungen",[568,1732,1734,1753],{"className":1733},[571],[568,1735,1737],{"className":1736},[575],[577,1738,1739],{"xmlns":579},[581,1740,1741,1750],{},[584,1742,1743],{},[1744,1745,1746,1748],"msub",{},[587,1747,743],{},[804,1749,1458],{},[591,1751,1752],{"encoding":593},"\\beta_1",[568,1754,1756],{"className":1755,"ariaHidden":598},[597],[568,1757,1759,1762],{"className":1758},[602],[568,1760],{"className":1761,"style":756},[606],[568,1763,1765,1768],{"className":1764},[611],[568,1766,743],{"className":1767,"style":769},[611,612],[568,1769,1771],{"className":1770},[878],[568,1772,1775,1799],{"className":1773},[882,1774],"vlist-t2",[568,1776,1778,1794],{"className":1777},[886],[568,1779,1782],{"className":1780,"style":1781},[890],"height:0.3011em;",[568,1783,1785,1788],{"style":1784},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[568,1786],{"className":1787,"style":899},[898],[568,1789,1791],{"className":1790},[903,904,905,906],[568,1792,1458],{"className":1793},[611,906],[568,1795,1798],{"className":1796},[1797],"vlist-s","​",[568,1800,1802],{"className":1801},[886],[568,1803,1806],{"className":1804,"style":1805},[890],"height:0.15em;",[568,1807],{},[568,1809,1811,1846],{"className":1810},[571],[568,1812,1814],{"className":1813},[575],[577,1815,1816],{"xmlns":579},[581,1817,1818,1843],{},[584,1819,1820,1827,1829,1835,1837],{},[1744,1821,1822,1824],{},[587,1823,743],{},[804,1825,1826],{},"2",[738,1828,791],{},[801,1830,1831,1833],{},[804,1832,806],{},[738,1834,809],{},[738,1836,812],{},[1744,1838,1839,1841],{},[587,1840,743],{},[804,1842,1458],{},[591,1844,1845],{"encoding":593},"\\beta_2 = 180^\\circ - \\beta_1",[568,1847,1849,1904,1952],{"className":1848,"ariaHidden":598},[597],[568,1850,1852,1855,1895,1898,1901],{"className":1851},[602],[568,1853],{"className":1854,"style":756},[606],[568,1856,1858,1861],{"className":1857},[611],[568,1859,743],{"className":1860,"style":769},[611,612],[568,1862,1864],{"className":1863},[878],[568,1865,1867,1887],{"className":1866},[882,1774],[568,1868,1870,1884],{"className":1869},[886],[568,1871,1873],{"className":1872,"style":1781},[890],[568,1874,1875,1878],{"style":1784},[568,1876],{"className":1877,"style":899},[898],[568,1879,1881],{"className":1880},[903,904,905,906],[568,1882,1826],{"className":1883},[611,906],[568,1885,1798],{"className":1886},[1797],[568,1888,1890],{"className":1889},[886],[568,1891,1893],{"className":1892,"style":1805},[890],[568,1894],{},[568,1896],{"className":1897,"style":842},[764],[568,1899,791],{"className":1900},[846],[568,1902],{"className":1903,"style":842},[764],[568,1905,1907,1911,1914,1943,1946,1949],{"className":1906},[602],[568,1908],{"className":1909,"style":1910},[606],"height:0.7574em;vertical-align:-0.0833em;",[568,1912,867],{"className":1913},[611],[568,1915,1917,1920],{"className":1916},[611],[568,1918,874],{"className":1919},[611],[568,1921,1923],{"className":1922},[878],[568,1924,1926],{"className":1925},[882],[568,1927,1929],{"className":1928},[886],[568,1930,1932],{"className":1931,"style":891},[890],[568,1933,1934,1937],{"style":894},[568,1935],{"className":1936,"style":899},[898],[568,1938,1940],{"className":1939},[903,904,905,906],[568,1941,809],{"className":1942},[910,906],[568,1944],{"className":1945,"style":914},[764],[568,1947,812],{"className":1948},[910],[568,1950],{"className":1951,"style":914},[764],[568,1953,1955,1958],{"className":1954},[602],[568,1956],{"className":1957,"style":756},[606],[568,1959,1961,1964],{"className":1960},[611],[568,1962,743],{"className":1963,"style":769},[611,612],[568,1965,1967],{"className":1966},[878],[568,1968,1970,1990],{"className":1969},[882,1774],[568,1971,1973,1987],{"className":1972},[886],[568,1974,1976],{"className":1975,"style":1781},[890],[568,1977,1978,1981],{"style":1784},[568,1979],{"className":1980,"style":899},[898],[568,1982,1984],{"className":1983},[903,904,905,906],[568,1985,1458],{"className":1986},[611,906],[568,1988,1798],{"className":1989},[1797],[568,1991,1993],{"className":1992},[886],[568,1994,1996],{"className":1995,"style":1805},[890],[568,1997],{},[939,1999,2000,1276,2050,2136],{},[568,2001,2003,2020],{"className":2002},[571],[568,2004,2006],{"className":2005},[575],[577,2007,2008],{"xmlns":579},[581,2009,2010,2018],{},[584,2011,2012,2014,2016],{},[587,2013,589],{},[738,2015,1151],{},[587,2017,628],{},[591,2019,1245],{"encoding":593},[568,2021,2023,2041],{"className":2022,"ariaHidden":598},[597],[568,2024,2026,2029,2032,2035,2038],{"className":2025},[602],[568,2027],{"className":2028,"style":972},[606],[568,2030,589],{"className":2031},[611,612],[568,2033],{"className":2034,"style":842},[764],[568,2036,1151],{"className":2037},[846],[568,2039],{"className":2040,"style":842},[764],[568,2042,2044,2047],{"className":2043},[602],[568,2045],{"className":2046,"style":640},[606],[568,2048,628],{"className":2049},[611,612],[568,2051,2053,2076],{"className":2052},[571],[568,2054,2056],{"className":2055},[575],[577,2057,2058],{"xmlns":579},[581,2059,2060,2073],{},[584,2061,2062,2064,2067],{},[587,2063,659],{},[738,2065,2066],{},"≥",[801,2068,2069,2071],{},[804,2070,1156],{},[738,2072,809],{},[591,2074,2075],{"encoding":593},"\\alpha \\ge 90^\\circ",[568,2077,2079,2098],{"className":2078,"ariaHidden":598},[597],[568,2080,2082,2086,2089,2092,2095],{"className":2081},[602],[568,2083],{"className":2084,"style":2085},[606],"height:0.7719em;vertical-align:-0.136em;",[568,2087,659],{"className":2088,"style":675},[611,612],[568,2090],{"className":2091,"style":842},[764],[568,2093,2066],{"className":2094},[846],[568,2096],{"className":2097,"style":842},[764],[568,2099,2101,2104,2107],{"className":2100},[602],[568,2102],{"className":2103,"style":891},[606],[568,2105,1192],{"className":2106},[611],[568,2108,2110,2113],{"className":2109},[611],[568,2111,874],{"className":2112},[611],[568,2114,2116],{"className":2115},[878],[568,2117,2119],{"className":2118},[882],[568,2120,2122],{"className":2121},[886],[568,2123,2125],{"className":2124,"style":891},[890],[568,2126,2127,2130],{"style":894},[568,2128],{"className":2129,"style":899},[898],[568,2131,2133],{"className":2132},[903,904,905,906],[568,2134,809],{"className":2135},[910,906],": keine Lösung.",[564,2138,2139,2140,1276,2272,1499],{},"Danach folgen ",[568,2141,2143,2174],{"className":2142},[571],[568,2144,2146],{"className":2145},[575],[577,2147,2148],{"xmlns":579},[581,2149,2150,2171],{},[584,2151,2152,2155,2157,2163,2165,2167,2169],{},[587,2153,2154],{},"γ",[738,2156,791],{},[801,2158,2159,2161],{},[804,2160,806],{},[738,2162,809],{},[738,2164,812],{},[587,2166,659],{},[738,2168,812],{},[587,2170,743],{},[591,2172,2173],{"encoding":593},"\\gamma = 180^\\circ - \\alpha - \\beta",[568,2175,2177,2197,2244,2263],{"className":2176,"ariaHidden":598},[597],[568,2178,2180,2184,2188,2191,2194],{"className":2179},[602],[568,2181],{"className":2182,"style":2183},[606],"height:0.625em;vertical-align:-0.1944em;",[568,2185,2154],{"className":2186,"style":2187},[611,612],"margin-right:0.0556em;",[568,2189],{"className":2190,"style":842},[764],[568,2192,791],{"className":2193},[846],[568,2195],{"className":2196,"style":842},[764],[568,2198,2200,2203,2206,2235,2238,2241],{"className":2199},[602],[568,2201],{"className":2202,"style":1910},[606],[568,2204,867],{"className":2205},[611],[568,2207,2209,2212],{"className":2208},[611],[568,2210,874],{"className":2211},[611],[568,2213,2215],{"className":2214},[878],[568,2216,2218],{"className":2217},[882],[568,2219,2221],{"className":2220},[886],[568,2222,2224],{"className":2223,"style":891},[890],[568,2225,2226,2229],{"style":894},[568,2227],{"className":2228,"style":899},[898],[568,2230,2232],{"className":2231},[903,904,905,906],[568,2233,809],{"className":2234},[910,906],[568,2236],{"className":2237,"style":914},[764],[568,2239,812],{"className":2240},[910],[568,2242],{"className":2243,"style":914},[764],[568,2245,2247,2251,2254,2257,2260],{"className":2246},[602],[568,2248],{"className":2249,"style":2250},[606],"height:0.6667em;vertical-align:-0.0833em;",[568,2252,659],{"className":2253,"style":675},[611,612],[568,2255],{"className":2256,"style":914},[764],[568,2258,812],{"className":2259},[910],[568,2261],{"className":2262,"style":914},[764],[568,2264,2266,2269],{"className":2265},[602],[568,2267],{"className":2268,"style":756},[606],[568,2270,743],{"className":2271,"style":769},[611,612],[568,2273,2275,2313],{"className":2274},[571],[568,2276,2278],{"className":2277},[575],[577,2279,2280],{"xmlns":579},[581,2281,2282,2310],{},[584,2283,2284,2287,2289],{},[587,2285,2286],{},"c",[738,2288,791],{},[2290,2291,2292,2302],"mfrac",{},[584,2293,2294,2296,2298,2300],{},[587,2295,589],{},[587,2297,736],{},[738,2299,740],{},[587,2301,2154],{},[584,2303,2304,2306,2308],{},[587,2305,736],{},[738,2307,740],{},[587,2309,659],{},[591,2311,2312],{"encoding":593},"c = \\frac{a \\sin \\gamma}{\\sin \\alpha}",[568,2314,2316,2334],{"className":2315,"ariaHidden":598},[597],[568,2317,2319,2322,2325,2328,2331],{"className":2318},[602],[568,2320],{"className":2321,"style":607},[606],[568,2323,2286],{"className":2324},[611,612],[568,2326],{"className":2327,"style":842},[764],[568,2329,791],{"className":2330},[846],[568,2332],{"className":2333,"style":842},[764],[568,2335,2337,2341],{"className":2336},[602],[568,2338],{"className":2339,"style":2340},[606],"height:1.2586em;vertical-align:-0.345em;",[568,2342,2344,2348,2455],{"className":2343},[611],[568,2345],{"className":2346},[863,2347],"nulldelimiter",[568,2349,2351],{"className":2350},[2290],[568,2352,2354,2446],{"className":2353},[882,1774],[568,2355,2357,2443],{"className":2356},[886],[568,2358,2361,2396,2407],{"className":2359,"style":2360},[890],"height:0.9136em;",[568,2362,2364,2368],{"style":2363},"top:-2.655em;",[568,2365],{"className":2366,"style":2367},[898],"height:3em;",[568,2369,2371],{"className":2370},[903,904,905,906],[568,2372,2374,2389,2393],{"className":2373},[611,906],[568,2375,2377,2381,2385],{"className":2376},[760,906],[568,2378,2380],{"className":2379},[906],"s",[568,2382,2384],{"className":2383},[906],"i",[568,2386,2388],{"className":2387},[906],"n",[568,2390],{"className":2391,"style":2392},[764,906],"margin-right:0.1952em;",[568,2394,659],{"className":2395,"style":675},[611,612,906],[568,2397,2399,2402],{"style":2398},"top:-3.23em;",[568,2400],{"className":2401,"style":2367},[898],[568,2403],{"className":2404,"style":2406},[2405],"frac-line","border-bottom-width:0.04em;",[568,2408,2410,2413],{"style":2409},"top:-3.4461em;",[568,2411],{"className":2412,"style":2367},[898],[568,2414,2416],{"className":2415},[903,904,905,906],[568,2417,2419,2422,2425,2437,2440],{"className":2418},[611,906],[568,2420,589],{"className":2421},[611,612,906],[568,2423],{"className":2424,"style":2392},[764,906],[568,2426,2428,2431,2434],{"className":2427},[760,906],[568,2429,2380],{"className":2430},[906],[568,2432,2384],{"className":2433},[906],[568,2435,2388],{"className":2436},[906],[568,2438],{"className":2439,"style":2392},[764,906],[568,2441,2154],{"className":2442,"style":2187},[611,612,906],[568,2444,1798],{"className":2445},[1797],[568,2447,2449],{"className":2448},[886],[568,2450,2453],{"className":2451,"style":2452},[890],"height:0.345em;",[568,2454],{},[568,2456],{"className":2457},[933,2347],[564,2459,2460,2461,2464,2465,2493,2494,2711,2712,2740,2741,3032],{},"Der ",[678,2462,2463],{},"Kosinussatz"," liefert ",[568,2466,2468,2481],{"className":2467},[571],[568,2469,2471],{"className":2470},[575],[577,2472,2473],{"xmlns":579},[581,2474,2475,2479],{},[584,2476,2477],{},[587,2478,2286],{},[591,2480,2286],{"encoding":593},[568,2482,2484],{"className":2483,"ariaHidden":598},[597],[568,2485,2487,2490],{"className":2486},[602],[568,2488],{"className":2489,"style":607},[606],[568,2491,2286],{"className":2492},[611,612]," direkt: Aus ",[568,2495,2497,2547],{"className":2496},[571],[568,2498,2500],{"className":2499},[575],[577,2501,2502],{"xmlns":579},[581,2503,2504,2544],{},[584,2505,2506,2512,2514,2520,2523,2529,2531,2533,2535,2537,2540,2542],{},[801,2507,2508,2510],{},[587,2509,589],{},[804,2511,1826],{},[738,2513,791],{},[801,2515,2516,2518],{},[587,2517,628],{},[804,2519,1826],{},[738,2521,2522],{},"+",[801,2524,2525,2527],{},[587,2526,2286],{},[804,2528,1826],{},[738,2530,812],{},[804,2532,1826],{},[587,2534,628],{},[587,2536,2286],{},[587,2538,2539],{},"cos",[738,2541,740],{},[587,2543,659],{},[591,2545,2546],{"encoding":593},"a^2 = b^2 + c^2 - 2bc\\cos\\alpha",[568,2548,2550,2595,2640,2684],{"className":2549,"ariaHidden":598},[597],[568,2551,2553,2557,2586,2589,2592],{"className":2552},[602],[568,2554],{"className":2555,"style":2556},[606],"height:0.8141em;",[568,2558,2560,2563],{"className":2559},[611],[568,2561,589],{"className":2562},[611,612],[568,2564,2566],{"className":2565},[878],[568,2567,2569],{"className":2568},[882],[568,2570,2572],{"className":2571},[886],[568,2573,2575],{"className":2574,"style":2556},[890],[568,2576,2577,2580],{"style":894},[568,2578],{"className":2579,"style":899},[898],[568,2581,2583],{"className":2582},[903,904,905,906],[568,2584,1826],{"className":2585},[611,906],[568,2587],{"className":2588,"style":842},[764],[568,2590,791],{"className":2591},[846],[568,2593],{"className":2594,"style":842},[764],[568,2596,2598,2602,2631,2634,2637],{"className":2597},[602],[568,2599],{"className":2600,"style":2601},[606],"height:0.8974em;vertical-align:-0.0833em;",[568,2603,2605,2608],{"className":2604},[611],[568,2606,628],{"className":2607},[611,612],[568,2609,2611],{"className":2610},[878],[568,2612,2614],{"className":2613},[882],[568,2615,2617],{"className":2616},[886],[568,2618,2620],{"className":2619,"style":2556},[890],[568,2621,2622,2625],{"style":894},[568,2623],{"className":2624,"style":899},[898],[568,2626,2628],{"className":2627},[903,904,905,906],[568,2629,1826],{"className":2630},[611,906],[568,2632],{"className":2633,"style":914},[764],[568,2635,2522],{"className":2636},[910],[568,2638],{"className":2639,"style":914},[764],[568,2641,2643,2646,2675,2678,2681],{"className":2642},[602],[568,2644],{"className":2645,"style":2601},[606],[568,2647,2649,2652],{"className":2648},[611],[568,2650,2286],{"className":2651},[611,612],[568,2653,2655],{"className":2654},[878],[568,2656,2658],{"className":2657},[882],[568,2659,2661],{"className":2660},[886],[568,2662,2664],{"className":2663,"style":2556},[890],[568,2665,2666,2669],{"style":894},[568,2667],{"className":2668,"style":899},[898],[568,2670,2672],{"className":2671},[903,904,905,906],[568,2673,1826],{"className":2674},[611,906],[568,2676],{"className":2677,"style":914},[764],[568,2679,812],{"className":2680},[910],[568,2682],{"className":2683,"style":914},[764],[568,2685,2687,2690,2693,2696,2699,2702,2705,2708],{"className":2686},[602],[568,2688],{"className":2689,"style":640},[606],[568,2691,1826],{"className":2692},[611],[568,2694,628],{"className":2695},[611,612],[568,2697,2286],{"className":2698},[611,612],[568,2700],{"className":2701,"style":765},[764],[568,2703,2539],{"className":2704},[760],[568,2706],{"className":2707,"style":765},[764],[568,2709,659],{"className":2710,"style":675},[611,612]," wird eine quadratische Gleichung in ",[568,2713,2715,2728],{"className":2714},[571],[568,2716,2718],{"className":2717},[575],[577,2719,2720],{"xmlns":579},[581,2721,2722,2726],{},[584,2723,2724],{},[587,2725,2286],{},[591,2727,2286],{"encoding":593},[568,2729,2731],{"className":2730,"ariaHidden":598},[597],[568,2732,2734,2737],{"className":2733},[602],[568,2735],{"className":2736,"style":607},[606],[568,2738,2286],{"className":2739},[611,612]," mit der Lösung ",[568,2742,2744,2802],{"className":2743},[571],[568,2745,2747],{"className":2746},[575],[577,2748,2749],{"xmlns":579},[581,2750,2751,2799],{},[584,2752,2753,2755,2757,2759,2761,2763,2765,2768],{},[587,2754,2286],{},[738,2756,791],{},[587,2758,628],{},[587,2760,2539],{},[738,2762,740],{},[587,2764,659],{},[738,2766,2767],{},"±",[2769,2770,2771],"msqrt",{},[584,2772,2773,2779,2781,2787,2797],{},[801,2774,2775,2777],{},[587,2776,589],{},[804,2778,1826],{},[738,2780,812],{},[801,2782,2783,2785],{},[587,2784,628],{},[804,2786,1826],{},[801,2788,2789,2795],{},[584,2790,2791,2793],{},[587,2792,736],{},[738,2794,740],{},[804,2796,1826],{},[587,2798,659],{},[591,2800,2801],{"encoding":593},"c = b\\cos\\alpha \\pm \\sqrt{a^2 - b^2\\sin^2\\alpha}",[568,2803,2805,2823,2854],{"className":2804,"ariaHidden":598},[597],[568,2806,2808,2811,2814,2817,2820],{"className":2807},[602],[568,2809],{"className":2810,"style":607},[606],[568,2812,2286],{"className":2813},[611,612],[568,2815],{"className":2816,"style":842},[764],[568,2818,791],{"className":2819},[846],[568,2821],{"className":2822,"style":842},[764],[568,2824,2826,2830,2833,2836,2839,2842,2845,2848,2851],{"className":2825},[602],[568,2827],{"className":2828,"style":2829},[606],"height:0.7778em;vertical-align:-0.0833em;",[568,2831,628],{"className":2832},[611,612],[568,2834],{"className":2835,"style":765},[764],[568,2837,2539],{"className":2838},[760],[568,2840],{"className":2841,"style":765},[764],[568,2843,659],{"className":2844,"style":675},[611,612],[568,2846],{"className":2847,"style":914},[764],[568,2849,2767],{"className":2850},[910],[568,2852],{"className":2853,"style":914},[764],[568,2855,2857,2861],{"className":2856},[602],[568,2858],{"className":2859,"style":2860},[606],"height:1.24em;vertical-align:-0.1607em;",[568,2862,2865],{"className":2863},[611,2864],"sqrt",[568,2866,2868,3023],{"className":2867},[882,1774],[568,2869,2871,3020],{"className":2870},[886],[568,2872,2875,2997],{"className":2873,"style":2874},[890],"height:1.0793em;",[568,2876,2880,2884],{"className":2877,"style":2879},[2878],"svg-align","top:-3.2em;",[568,2881],{"className":2882,"style":2883},[898],"height:3.2em;",[568,2885,2888,2919,2922,2925,2928,2957,2960,2991,2994],{"className":2886,"style":2887},[611],"padding-left:1em;",[568,2889,2891,2894],{"className":2890},[611],[568,2892,589],{"className":2893},[611,612],[568,2895,2897],{"className":2896},[878],[568,2898,2900],{"className":2899},[882],[568,2901,2903],{"className":2902},[886],[568,2904,2907],{"className":2905,"style":2906},[890],"height:0.7401em;",[568,2908,2910,2913],{"style":2909},"top:-2.989em;margin-right:0.05em;",[568,2911],{"className":2912,"style":899},[898],[568,2914,2916],{"className":2915},[903,904,905,906],[568,2917,1826],{"className":2918},[611,906],[568,2920],{"className":2921,"style":914},[764],[568,2923,812],{"className":2924},[910],[568,2926],{"className":2927,"style":914},[764],[568,2929,2931,2934],{"className":2930},[611],[568,2932,628],{"className":2933},[611,612],[568,2935,2937],{"className":2936},[878],[568,2938,2940],{"className":2939},[882],[568,2941,2943],{"className":2942},[886],[568,2944,2946],{"className":2945,"style":2906},[890],[568,2947,2948,2951],{"style":2909},[568,2949],{"className":2950,"style":899},[898],[568,2952,2954],{"className":2953},[903,904,905,906],[568,2955,1826],{"className":2956},[611,906],[568,2958],{"className":2959,"style":765},[764],[568,2961,2963,2966],{"className":2962},[760],[568,2964,736],{"className":2965},[760],[568,2967,2969],{"className":2968},[878],[568,2970,2972],{"className":2971},[882],[568,2973,2975],{"className":2974},[886],[568,2976,2979],{"className":2977,"style":2978},[890],"height:0.8719em;",[568,2980,2982,2985],{"style":2981},"top:-3.1208em;margin-right:0.05em;",[568,2983],{"className":2984,"style":899},[898],[568,2986,2988],{"className":2987},[903,904,905,906],[568,2989,1826],{"className":2990},[611,906],[568,2992],{"className":2993,"style":765},[764],[568,2995,659],{"className":2996,"style":675},[611,612],[568,2998,3000,3003],{"style":2999},"top:-3.0393em;",[568,3001],{"className":3002,"style":2883},[898],[568,3004,3008],{"className":3005,"style":3007},[3006],"hide-tail","min-width:1.02em;height:1.28em;",[3009,3010,3016],"svg",{"xmlns":3011,"width":3012,"height":3013,"viewBox":3014,"preserveAspectRatio":3015},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[3017,3018],"path",{"d":3019},"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",[568,3021,1798],{"className":3022},[1797],[568,3024,3026],{"className":3025},[886],[568,3027,3030],{"className":3028,"style":3029},[890],"height:0.1607em;",[568,3031],{},". Gültig sind nur positive Werte. Die Anzahl positiver Lösungen ist genau die Anzahl der Dreiecke.",[559,3034,3036],{"id":3035},"beispiele","Beispiele",[564,3038,3039,3042,3043,613,3095,613,3147,3232,3233,1499],{},[678,3040,3041],{},"Eine Lösung:"," ",[568,3044,3046,3065],{"className":3045},[571],[568,3047,3049],{"className":3048},[575],[577,3050,3051],{"xmlns":579},[581,3052,3053,3062],{},[584,3054,3055,3057,3059],{},[587,3056,589],{},[738,3058,791],{},[804,3060,3061],{},"8",[591,3063,3064],{"encoding":593},"a = 8",[568,3066,3068,3086],{"className":3067,"ariaHidden":598},[597],[568,3069,3071,3074,3077,3080,3083],{"className":3070},[602],[568,3072],{"className":3073,"style":607},[606],[568,3075,589],{"className":3076},[611,612],[568,3078],{"className":3079,"style":842},[764],[568,3081,791],{"className":3082},[846],[568,3084],{"className":3085,"style":842},[764],[568,3087,3089,3092],{"className":3088},[602],[568,3090],{"className":3091,"style":1495},[606],[568,3093,3061],{"className":3094},[611],[568,3096,3098,3117],{"className":3097},[571],[568,3099,3101],{"className":3100},[575],[577,3102,3103],{"xmlns":579},[581,3104,3105,3114],{},[584,3106,3107,3109,3111],{},[587,3108,628],{},[738,3110,791],{},[804,3112,3113],{},"5",[591,3115,3116],{"encoding":593},"b = 5",[568,3118,3120,3138],{"className":3119,"ariaHidden":598},[597],[568,3121,3123,3126,3129,3132,3135],{"className":3122},[602],[568,3124],{"className":3125,"style":640},[606],[568,3127,628],{"className":3128},[611,612],[568,3130],{"className":3131,"style":842},[764],[568,3133,791],{"className":3134},[846],[568,3136],{"className":3137,"style":842},[764],[568,3139,3141,3144],{"className":3140},[602],[568,3142],{"className":3143,"style":1495},[606],[568,3145,3113],{"className":3146},[611],[568,3148,3150,3173],{"className":3149},[571],[568,3151,3153],{"className":3152},[575],[577,3154,3155],{"xmlns":579},[581,3156,3157,3170],{},[584,3158,3159,3161,3163],{},[587,3160,659],{},[738,3162,791],{},[801,3164,3165,3168],{},[804,3166,3167],{},"50",[738,3169,809],{},[591,3171,3172],{"encoding":593},"\\alpha = 50^\\circ",[568,3174,3176,3194],{"className":3175,"ariaHidden":598},[597],[568,3177,3179,3182,3185,3188,3191],{"className":3178},[602],[568,3180],{"className":3181,"style":607},[606],[568,3183,659],{"className":3184,"style":675},[611,612],[568,3186],{"className":3187,"style":842},[764],[568,3189,791],{"className":3190},[846],[568,3192],{"className":3193,"style":842},[764],[568,3195,3197,3200,3203],{"className":3196},[602],[568,3198],{"className":3199,"style":891},[606],[568,3201,3113],{"className":3202},[611],[568,3204,3206,3209],{"className":3205},[611],[568,3207,874],{"className":3208},[611],[568,3210,3212],{"className":3211},[878],[568,3213,3215],{"className":3214},[882],[568,3216,3218],{"className":3217},[886],[568,3219,3221],{"className":3220,"style":891},[890],[568,3222,3223,3226],{"style":894},[568,3224],{"className":3225,"style":899},[898],[568,3227,3229],{"className":3228},[903,904,905,906],[568,3230,809],{"className":3231},[910,906],". Hier ist ",[568,3234,3236,3253],{"className":3235},[571],[568,3237,3239],{"className":3238},[575],[577,3240,3241],{"xmlns":579},[581,3242,3243,3251],{},[584,3244,3245,3247,3249],{},[587,3246,589],{},[738,3248,957],{},[587,3250,628],{},[591,3252,962],{"encoding":593},[568,3254,3256,3274],{"className":3255,"ariaHidden":598},[597],[568,3257,3259,3262,3265,3268,3271],{"className":3258},[602],[568,3260],{"className":3261,"style":972},[606],[568,3263,589],{"className":3264},[611,612],[568,3266],{"className":3267,"style":842},[764],[568,3269,957],{"className":3270},[846],[568,3272],{"className":3273,"style":842},[764],[568,3275,3277,3280],{"className":3276},[602],[568,3278],{"className":3279,"style":640},[606],[568,3281,628],{"className":3282},[611,612],[568,3284,3287],{"className":3285},[3286],"katex-display",[568,3288,3290,3354],{"className":3289},[571],[568,3291,3293],{"className":3292},[575],[577,3294,3296],{"xmlns":579,"display":3295},"block",[581,3297,3298,3351],{},[584,3299,3300,3302,3304,3306,3308,3326,3329,3332,3335,3338,3340,3342,3344],{},[587,3301,736],{},[738,3303,740],{},[587,3305,743],{},[738,3307,791],{},[2290,3309,3310,3324],{},[584,3311,3312,3314,3316,3318],{},[804,3313,3113],{},[587,3315,736],{},[738,3317,740],{},[801,3319,3320,3322],{},[804,3321,3167],{},[738,3323,809],{},[804,3325,3061],{},[738,3327,3328],{},"≈",[804,3330,3331],{},"0,4788",[764,3333],{"width":3334},"1em",[738,3336,3337],{},"⇒",[764,3339],{"width":3334},[587,3341,743],{},[738,3343,3328],{},[801,3345,3346,3349],{},[804,3347,3348],{},"28,6",[738,3350,809],{},[591,3352,3353],{"encoding":593},"\\sin \\beta = \\frac{5 \\sin 50^\\circ}{8} \\approx 0{,}4788 \\quad\\Rightarrow\\quad \\beta \\approx 28{,}6^\\circ",[568,3355,3357,3381,3504,3542,3560],{"className":3356,"ariaHidden":598},[597],[568,3358,3360,3363,3366,3369,3372,3375,3378],{"className":3359},[602],[568,3361],{"className":3362,"style":756},[606],[568,3364,736],{"className":3365},[760],[568,3367],{"className":3368,"style":765},[764],[568,3370,743],{"className":3371,"style":769},[611,612],[568,3373],{"className":3374,"style":842},[764],[568,3376,791],{"className":3377},[846],[568,3379],{"className":3380,"style":842},[764],[568,3382,3384,3388,3495,3498,3501],{"className":3383},[602],[568,3385],{"className":3386,"style":3387},[606],"height:2.0371em;vertical-align:-0.686em;",[568,3389,3391,3394,3492],{"className":3390},[611],[568,3392],{"className":3393},[863,2347],[568,3395,3397],{"className":3396},[2290],[568,3398,3400,3483],{"className":3399},[882,1774],[568,3401,3403,3480],{"className":3402},[886],[568,3404,3407,3419,3427],{"className":3405,"style":3406},[890],"height:1.3511em;",[568,3408,3410,3413],{"style":3409},"top:-2.314em;",[568,3411],{"className":3412,"style":2367},[898],[568,3414,3416],{"className":3415},[611],[568,3417,3061],{"className":3418},[611],[568,3420,3421,3424],{"style":2398},[568,3422],{"className":3423,"style":2367},[898],[568,3425],{"className":3426,"style":2406},[2405],[568,3428,3430,3433],{"style":3429},"top:-3.677em;",[568,3431],{"className":3432,"style":2367},[898],[568,3434,3436,3439,3442,3445,3448,3451],{"className":3435},[611],[568,3437,3113],{"className":3438},[611],[568,3440],{"className":3441,"style":765},[764],[568,3443,736],{"className":3444},[760],[568,3446],{"className":3447,"style":765},[764],[568,3449,3113],{"className":3450},[611],[568,3452,3454,3457],{"className":3453},[611],[568,3455,874],{"className":3456},[611],[568,3458,3460],{"className":3459},[878],[568,3461,3463],{"className":3462},[882],[568,3464,3466],{"className":3465},[886],[568,3467,3469],{"className":3468,"style":891},[890],[568,3470,3471,3474],{"style":894},[568,3472],{"className":3473,"style":899},[898],[568,3475,3477],{"className":3476},[903,904,905,906],[568,3478,809],{"className":3479},[910,906],[568,3481,1798],{"className":3482},[1797],[568,3484,3486],{"className":3485},[886],[568,3487,3490],{"className":3488,"style":3489},[890],"height:0.686em;",[568,3491],{},[568,3493],{"className":3494},[933,2347],[568,3496],{"className":3497,"style":842},[764],[568,3499,3328],{"className":3500},[846],[568,3502],{"className":3503,"style":842},[764],[568,3505,3507,3511,3514,3522,3526,3530,3533,3536,3539],{"className":3506},[602],[568,3508],{"className":3509,"style":3510},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,3512,874],{"className":3513},[611],[568,3515,3517],{"className":3516},[611],[568,3518,3521],{"className":3519},[3520],"mpunct",",",[568,3523,3525],{"className":3524},[611],"4788",[568,3527],{"className":3528,"style":3529},[764],"margin-right:1em;",[568,3531],{"className":3532,"style":842},[764],[568,3534,3337],{"className":3535},[846],[568,3537],{"className":3538,"style":3529},[764],[568,3540],{"className":3541,"style":842},[764],[568,3543,3545,3548,3551,3554,3557],{"className":3544},[602],[568,3546],{"className":3547,"style":756},[606],[568,3549,743],{"className":3550,"style":769},[611,612],[568,3552],{"className":3553,"style":842},[764],[568,3555,3328],{"className":3556},[846],[568,3558],{"className":3559,"style":842},[764],[568,3561,3563,3567,3571,3577],{"className":3562},[602],[568,3564],{"className":3565,"style":3566},[606],"height:0.9186em;vertical-align:-0.1944em;",[568,3568,3570],{"className":3569},[611],"28",[568,3572,3574],{"className":3573},[611],[568,3575,3521],{"className":3576},[3520],[568,3578,3580,3584],{"className":3579},[611],[568,3581,3583],{"className":3582},[611],"6",[568,3585,3587],{"className":3586},[878],[568,3588,3590],{"className":3589},[882],[568,3591,3593],{"className":3592},[886],[568,3594,3597],{"className":3595,"style":3596},[890],"height:0.7241em;",[568,3598,3600,3603],{"style":3599},"top:-3.113em;margin-right:0.05em;",[568,3601],{"className":3602,"style":899},[898],[568,3604,3606],{"className":3605},[903,904,905,906],[568,3607,809],{"className":3608},[910,906],[564,3610,3611,1276,3706,3948,3949,3977,3978,1499],{},[568,3612,3614,3637],{"className":3613},[571],[568,3615,3617],{"className":3616},[575],[577,3618,3619],{"xmlns":579},[581,3620,3621,3634],{},[584,3622,3623,3625,3627],{},[587,3624,2154],{},[738,3626,3328],{},[801,3628,3629,3632],{},[804,3630,3631],{},"101,4",[738,3633,809],{},[591,3635,3636],{"encoding":593},"\\gamma \\approx 101{,}4^\\circ",[568,3638,3640,3659],{"className":3639,"ariaHidden":598},[597],[568,3641,3643,3647,3650,3653,3656],{"className":3642},[602],[568,3644],{"className":3645,"style":3646},[606],"height:0.6776em;vertical-align:-0.1944em;",[568,3648,2154],{"className":3649,"style":2187},[611,612],[568,3651],{"className":3652,"style":842},[764],[568,3654,3328],{"className":3655},[846],[568,3657],{"className":3658,"style":842},[764],[568,3660,3662,3666,3670,3676],{"className":3661},[602],[568,3663],{"className":3664,"style":3665},[606],"height:0.8686em;vertical-align:-0.1944em;",[568,3667,3669],{"className":3668},[611],"101",[568,3671,3673],{"className":3672},[611],[568,3674,3521],{"className":3675},[3520],[568,3677,3679,3683],{"className":3678},[611],[568,3680,3682],{"className":3681},[611],"4",[568,3684,3686],{"className":3685},[878],[568,3687,3689],{"className":3688},[882],[568,3690,3692],{"className":3691},[886],[568,3693,3695],{"className":3694,"style":891},[890],[568,3696,3697,3700],{"style":894},[568,3698],{"className":3699,"style":899},[898],[568,3701,3703],{"className":3702},[903,904,905,906],[568,3704,809],{"className":3705},[910,906],[568,3707,3709,3754],{"className":3708},[571],[568,3710,3712],{"className":3711},[575],[577,3713,3714],{"xmlns":579},[581,3715,3716,3751],{},[584,3717,3718,3720,3722,3746,3748],{},[587,3719,2286],{},[738,3721,791],{},[2290,3723,3724,3734],{},[584,3725,3726,3728,3730,3732],{},[804,3727,3061],{},[587,3729,736],{},[738,3731,740],{},[587,3733,2154],{},[584,3735,3736,3738,3740],{},[587,3737,736],{},[738,3739,740],{},[801,3741,3742,3744],{},[804,3743,3167],{},[738,3745,809],{},[738,3747,3328],{},[804,3749,3750],{},"10,24",[591,3752,3753],{"encoding":593},"c = \\frac{8 \\sin \\gamma}{\\sin 50^\\circ} \\approx 10{,}24",[568,3755,3757,3775,3928],{"className":3756,"ariaHidden":598},[597],[568,3758,3760,3763,3766,3769,3772],{"className":3759},[602],[568,3761],{"className":3762,"style":607},[606],[568,3764,2286],{"className":3765},[611,612],[568,3767],{"className":3768,"style":842},[764],[568,3770,791],{"className":3771},[846],[568,3773],{"className":3774,"style":842},[764],[568,3776,3778,3781,3919,3922,3925],{"className":3777},[602],[568,3779],{"className":3780,"style":2340},[606],[568,3782,3784,3787,3916],{"className":3783},[611],[568,3785],{"className":3786},[863,2347],[568,3788,3790],{"className":3789},[2290],[568,3791,3793,3908],{"className":3792},[882,1774],[568,3794,3796,3905],{"className":3795},[886],[568,3797,3799,3862,3870],{"className":3798,"style":2360},[890],[568,3800,3801,3804],{"style":2363},[568,3802],{"className":3803,"style":2367},[898],[568,3805,3807],{"className":3806},[903,904,905,906],[568,3808,3810,3822,3825,3828],{"className":3809},[611,906],[568,3811,3813,3816,3819],{"className":3812},[760,906],[568,3814,2380],{"className":3815},[906],[568,3817,2384],{"className":3818},[906],[568,3820,2388],{"className":3821},[906],[568,3823],{"className":3824,"style":2392},[764,906],[568,3826,3113],{"className":3827},[611,906],[568,3829,3831,3834],{"className":3830},[611,906],[568,3832,874],{"className":3833},[611,906],[568,3835,3837],{"className":3836},[878],[568,3838,3840],{"className":3839},[882],[568,3841,3843],{"className":3842},[886],[568,3844,3847],{"className":3845,"style":3846},[890],"height:0.6035em;",[568,3848,3850,3854],{"style":3849},"top:-2.786em;margin-right:0.0714em;",[568,3851],{"className":3852,"style":3853},[898],"height:2.5em;",[568,3855,3859],{"className":3856},[903,3857,3858,906],"reset-size3","size1",[568,3860,809],{"className":3861},[910,906],[568,3863,3864,3867],{"style":2398},[568,3865],{"className":3866,"style":2367},[898],[568,3868],{"className":3869,"style":2406},[2405],[568,3871,3872,3875],{"style":2409},[568,3873],{"className":3874,"style":2367},[898],[568,3876,3878],{"className":3877},[903,904,905,906],[568,3879,3881,3884,3887,3899,3902],{"className":3880},[611,906],[568,3882,3061],{"className":3883},[611,906],[568,3885],{"className":3886,"style":2392},[764,906],[568,3888,3890,3893,3896],{"className":3889},[760,906],[568,3891,2380],{"className":3892},[906],[568,3894,2384],{"className":3895},[906],[568,3897,2388],{"className":3898},[906],[568,3900],{"className":3901,"style":2392},[764,906],[568,3903,2154],{"className":3904,"style":2187},[611,612,906],[568,3906,1798],{"className":3907},[1797],[568,3909,3911],{"className":3910},[886],[568,3912,3914],{"className":3913,"style":2452},[890],[568,3915],{},[568,3917],{"className":3918},[933,2347],[568,3920],{"className":3921,"style":842},[764],[568,3923,3328],{"className":3924},[846],[568,3926],{"className":3927,"style":842},[764],[568,3929,3931,3934,3938,3944],{"className":3930},[602],[568,3932],{"className":3933,"style":3510},[606],[568,3935,3937],{"className":3936},[611],"10",[568,3939,3941],{"className":3940},[611],[568,3942,3521],{"className":3943},[3520],[568,3945,3947],{"className":3946},[611],"24",". Der Kosinussatz bestätigt das: Nur die Lösung mit ",[568,3950,3952,3965],{"className":3951},[571],[568,3953,3955],{"className":3954},[575],[577,3956,3957],{"xmlns":579},[581,3958,3959,3963],{},[584,3960,3961],{},[738,3962,2522],{},[591,3964,2522],{"encoding":593},[568,3966,3968],{"className":3967,"ariaHidden":598},[597],[568,3969,3971,3974],{"className":3970},[602],[568,3972],{"className":3973,"style":2250},[606],[568,3975,2522],{"className":3976},[611]," ist positiv, ",[568,3979,3981,3999],{"className":3980},[571],[568,3982,3984],{"className":3983},[575],[577,3985,3986],{"xmlns":579},[581,3987,3988,3996],{},[584,3989,3990,3992,3994],{},[587,3991,2286],{},[738,3993,3328],{},[804,3995,3750],{},[591,3997,3998],{"encoding":593},"c \\approx 10{,}24",[568,4000,4002,4021],{"className":4001,"ariaHidden":598},[597],[568,4003,4005,4009,4012,4015,4018],{"className":4004},[602],[568,4006],{"className":4007,"style":4008},[606],"height:0.4831em;",[568,4010,2286],{"className":4011},[611,612],[568,4013],{"className":4014,"style":842},[764],[568,4016,3328],{"className":4017},[846],[568,4019],{"className":4020,"style":842},[764],[568,4022,4024,4027,4030,4036],{"className":4023},[602],[568,4025],{"className":4026,"style":3510},[606],[568,4028,3937],{"className":4029},[611],[568,4031,4033],{"className":4032},[611],[568,4034,3521],{"className":4035},[3520],[568,4037,3947],{"className":4038},[611],[564,4040,4041,3042,4044,613,4095,613,4146,3232,4231,1499],{},[678,4042,4043],{},"Zwei Lösungen:",[568,4045,4047,4065],{"className":4046},[571],[568,4048,4050],{"className":4049},[575],[577,4051,4052],{"xmlns":579},[581,4053,4054,4062],{},[584,4055,4056,4058,4060],{},[587,4057,589],{},[738,4059,791],{},[804,4061,3583],{},[591,4063,4064],{"encoding":593},"a = 6",[568,4066,4068,4086],{"className":4067,"ariaHidden":598},[597],[568,4069,4071,4074,4077,4080,4083],{"className":4070},[602],[568,4072],{"className":4073,"style":607},[606],[568,4075,589],{"className":4076},[611,612],[568,4078],{"className":4079,"style":842},[764],[568,4081,791],{"className":4082},[846],[568,4084],{"className":4085,"style":842},[764],[568,4087,4089,4092],{"className":4088},[602],[568,4090],{"className":4091,"style":1495},[606],[568,4093,3583],{"className":4094},[611],[568,4096,4098,4116],{"className":4097},[571],[568,4099,4101],{"className":4100},[575],[577,4102,4103],{"xmlns":579},[581,4104,4105,4113],{},[584,4106,4107,4109,4111],{},[587,4108,628],{},[738,4110,791],{},[804,4112,3061],{},[591,4114,4115],{"encoding":593},"b = 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40^\\circ",[568,4173,4175,4193],{"className":4174,"ariaHidden":598},[597],[568,4176,4178,4181,4184,4187,4190],{"className":4177},[602],[568,4179],{"className":4180,"style":607},[606],[568,4182,659],{"className":4183,"style":675},[611,612],[568,4185],{"className":4186,"style":842},[764],[568,4188,791],{"className":4189},[846],[568,4191],{"className":4192,"style":842},[764],[568,4194,4196,4199,4202],{"className":4195},[602],[568,4197],{"className":4198,"style":891},[606],[568,4200,3682],{"className":4201},[611],[568,4203,4205,4208],{"className":4204},[611],[568,4206,874],{"className":4207},[611],[568,4209,4211],{"className":4210},[878],[568,4212,4214],{"className":4213},[882],[568,4215,4217],{"className":4216},[886],[568,4218,4220],{"className":4219,"style":891},[890],[568,4221,4222,4225],{"style":894},[568,4223],{"className":4224,"style":899},[898],[568,4226,4228],{"className":4227},[903,904,905,906],[568,4229,809],{"className":4230},[910,906],[568,4232,4234,4263],{"className":4233},[571],[568,4235,4237],{"className":4236},[575],[577,4238,4239],{"xmlns":579},[581,4240,4241,4260],{},[584,4242,4243,4245,4247,4249,4251,4253,4256,4258],{},[587,4244,628],{},[587,4246,736],{},[738,4248,740],{},[587,4250,659],{},[738,4252,3328],{},[804,4254,4255],{},"5,14",[738,4257,1151],{},[804,4259,3583],{},[591,4261,4262],{"encoding":593},"b \\sin \\alpha \\approx 5{,}14 \u003C 6",[568,4264,4266,4296,4324],{"className":4265,"ariaHidden":598},[597],[568,4267,4269,4272,4275,4278,4281,4284,4287,4290,4293],{"className":4268},[602],[568,4270],{"className":4271,"style":640},[606],[568,4273,628],{"className":4274},[611,612],[568,4276],{"className":4277,"style":765},[764],[568,4279,736],{"className":4280},[760],[568,4282],{"className":4283,"style":765},[764],[568,4285,659],{"className":4286,"style":675},[611,612],[568,4288],{"className":4289,"style":842},[764],[568,4291,3328],{"className":4292},[846],[568,4294],{"className":4295,"style":842},[764],[568,4297,4299,4302,4305,4311,4315,4318,4321],{"className":4298},[602],[568,4300],{"className":4301,"style":3510},[606],[568,4303,3113],{"className":4304},[611],[568,4306,4308],{"className":4307},[611],[568,4309,3521],{"className":4310},[3520],[568,4312,4314],{"className":4313},[611],"14",[568,4316],{"className":4317,"style":842},[764],[568,4319,1151],{"className":4320},[846],[568,4322],{"className":4323,"style":842},[764],[568,4325,4327,4330],{"className":4326},[602],[568,4328],{"className":4329,"style":1495},[606],[568,4331,3583],{"className":4332},[611],[568,4334,4336],{"className":4335},[3286],[568,4337,4339,4422],{"className":4338},[571],[568,4340,4342],{"className":4341},[575],[577,4343,4344],{"xmlns":579,"display":3295},[581,4345,4346,4419],{},[584,4347,4348,4350,4352,4354,4356,4374,4376,4379,4381,4383,4385,4391,4393,4400,4402,4404,4410,4412],{},[587,4349,736],{},[738,4351,740],{},[587,4353,743],{},[738,4355,791],{},[2290,4357,4358,4372],{},[584,4359,4360,4362,4364,4366],{},[804,4361,3061],{},[587,4363,736],{},[738,4365,740],{},[801,4367,4368,4370],{},[804,4369,4166],{},[738,4371,809],{},[804,4373,3583],{},[738,4375,3328],{},[804,4377,4378],{},"0,8571",[764,4380],{"width":3334},[738,4382,3337],{},[764,4384],{"width":3334},[1744,4386,4387,4389],{},[587,4388,743],{},[804,4390,1458],{},[738,4392,3328],{},[801,4394,4395,4398],{},[804,4396,4397],{},"59,0",[738,4399,809],{},[738,4401,3521],{"separator":598},[764,4403],{"width":3334},[1744,4405,4406,4408],{},[587,4407,743],{},[804,4409,1826],{},[738,4411,3328],{},[801,4413,4414,4417],{},[804,4415,4416],{},"121,0",[738,4418,809],{},[591,4420,4421],{"encoding":593},"\\sin \\beta = \\frac{8 \\sin 40^\\circ}{6} \\approx 0{,}8571 \\quad\\Rightarrow\\quad \\beta_1 \\approx 59{,}0^\\circ, \\quad \\beta_2 \\approx 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dem Kosinussatz: ",[568,4808,4810,4868],{"className":4809},[571],[568,4811,4813],{"className":4812},[575],[577,4814,4815],{"xmlns":579},[581,4816,4817,4865],{},[584,4818,4819,4821,4823,4825,4827,4829,4835,4837],{},[587,4820,2286],{},[738,4822,791],{},[804,4824,3061],{},[587,4826,2539],{},[738,4828,740],{},[801,4830,4831,4833],{},[804,4832,4166],{},[738,4834,809],{},[738,4836,2767],{},[2769,4838,4839],{},[584,4840,4841,4844,4846,4849,4859],{},[804,4842,4843],{},"36",[738,4845,812],{},[804,4847,4848],{},"64",[801,4850,4851,4857],{},[584,4852,4853,4855],{},[587,4854,736],{},[738,4856,740],{},[804,4858,1826],{},[801,4860,4861,4863],{},[804,4862,4166],{},[738,4864,809],{},[591,4866,4867],{"encoding":593},"c = 8\\cos 40^\\circ \\pm \\sqrt{36 - 64 \\sin^2 40^\\circ}",[568,4869,4871,4889,4948],{"className":4870,"ariaHidden":598},[597],[568,4872,4874,4877,4880,4883,4886],{"className":4873},[602],[568,4875],{"className":4876,"style":607},[606],[568,4878,2286],{"className":4879},[611,612],[568,4881],{"className":4882,"style":842},[764],[568,4884,791],{"className":4885},[846],[568,4887],{"className":4888,"style":842},[764],[568,4890,4892,4895,4898,4901,4904,4907,4910,4939,4942,4945],{"className":4891},[602],[568,4893],{"className":4894,"style":1910},[606],[568,4896,3061],{"className":4897},[611],[568,4899],{"className":4900,"style":765},[764],[568,4902,2539],{"className":4903},[760],[568,4905],{"className":4906,"style":765},[764],[568,4908,3682],{"className":4909},[611],[568,4911,4913,4916],{"className":4912},[611],[568,4914,874],{"className":4915},[611],[568,4917,4919],{"className":4918},[878],[568,4920,4922],{"className":4921},[882],[568,4923,4925],{"className":4924},[886],[568,4926,4928],{"className":4927,"style":891},[890],[568,4929,4930,4933],{"style":894},[568,4931],{"className":4932,"style":899},[898],[568,4934,4936],{"className":4935},[903,904,905,906],[568,4937,809],{"className":4938},[910,906],[568,4940],{"className":4941,"style":914},[764],[568,4943,2767],{"className":4944},[910],[568,4946],{"className":4947,"style":914},[764],[568,4949,4951,4954],{"className":4950},[602],[568,4952],{"className":4953,"style":2860},[606],[568,4955,4957],{"className":4956},[611,2864],[568,4958,4960,5073],{"className":4959},[882,1774],[568,4961,4963,5070],{"className":4962},[886],[568,4964,4966,5058],{"className":4965,"style":2874},[890],[568,4967,4969,4972],{"className":4968,"style":2879},[2878],[568,4970],{"className":4971,"style":2883},[898],[568,4973,4975,4978,4981,4984,4987,4990,4993,5022,5025,5028],{"className":4974,"style":2887},[611],[568,4976,4843],{"className":4977},[611],[568,4979],{"className":4980,"style":914},[764],[568,4982,812],{"className":4983},[910],[568,4985],{"className":4986,"style":914},[764],[568,4988,4848],{"className":4989},[611],[568,4991],{"className":4992,"style":765},[764],[568,4994,4996,4999],{"className":4995},[760],[568,4997,736],{"className":4998},[760],[568,5000,5002],{"className":5001},[878],[568,5003,5005],{"className":5004},[882],[568,5006,5008],{"className":5007},[886],[568,5009,5011],{"className":5010,"style":2978},[890],[568,5012,5013,5016],{"style":2981},[568,5014],{"className":5015,"style":899},[898],[568,5017,5019],{"className":5018},[903,904,905,906],[568,5020,1826],{"className":5021},[611,906],[568,5023],{"className":5024,"style":765},[764],[568,5026,3682],{"className":5027},[611],[568,5029,5031,5034],{"className":5030},[611],[568,5032,874],{"className":5033},[611],[568,5035,5037],{"className":5036},[878],[568,5038,5040],{"className":5039},[882],[568,5041,5043],{"className":5042},[886],[568,5044,5047],{"className":5045,"style":5046},[890],"height:0.6001em;",[568,5048,5049,5052],{"style":2909},[568,5050],{"className":5051,"style":899},[898],[568,5053,5055],{"className":5054},[903,904,905,906],[568,5056,809],{"className":5057},[910,906],[568,5059,5060,5063],{"style":2999},[568,5061],{"className":5062,"style":2883},[898],[568,5064,5066],{"className":5065,"style":3007},[3006],[3009,5067,5068],{"xmlns":3011,"width":3012,"height":3013,"viewBox":3014,"preserveAspectRatio":3015},[3017,5069],{"d":3019},[568,5071,1798],{"className":5072},[1797],[568,5074,5076],{"className":5075},[886],[568,5077,5079],{"className":5078,"style":3029},[890],[568,5080],{},", also ",[568,5083,5085,5108],{"className":5084},[571],[568,5086,5088],{"className":5087},[575],[577,5089,5090],{"xmlns":579},[581,5091,5092,5105],{},[584,5093,5094,5100,5102],{},[1744,5095,5096,5098],{},[587,5097,2286],{},[804,5099,1458],{},[738,5101,3328],{},[804,5103,5104],{},"9,22",[591,5106,5107],{"encoding":593},"c_1 \\approx 9{,}22",[568,5109,5111,5168],{"className":5110,"ariaHidden":598},[597],[568,5112,5114,5118,5159,5162,5165],{"className":5113},[602],[568,5115],{"className":5116,"style":5117},[606],"height:0.6331em;vertical-align:-0.15em;",[568,5119,5121,5124],{"className":5120},[611],[568,5122,2286],{"className":5123},[611,612],[568,5125,5127],{"className":5126},[878],[568,5128,5130,5151],{"className":5129},[882,1774],[568,5131,5133,5148],{"className":5132},[886],[568,5134,5136],{"className":5135,"style":1781},[890],[568,5137,5139,5142],{"style":5138},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[568,5140],{"className":5141,"style":899},[898],[568,5143,5145],{"className":5144},[903,904,905,906],[568,5146,1458],{"className":5147},[611,906],[568,5149,1798],{"className":5150},[1797],[568,5152,5154],{"className":5153},[886],[568,5155,5157],{"className":5156,"style":1805},[890],[568,5158],{},[568,5160],{"className":5161,"style":842},[764],[568,5163,3328],{"className":5164},[846],[568,5166],{"className":5167,"style":842},[764],[568,5169,5171,5174,5177,5183],{"className":5170},[602],[568,5172],{"className":5173,"style":3510},[606],[568,5175,1192],{"className":5176},[611],[568,5178,5180],{"className":5179},[611],[568,5181,3521],{"className":5182},[3520],[568,5184,5186],{"className":5185},[611],"22",[568,5188,5190,5213],{"className":5189},[571],[568,5191,5193],{"className":5192},[575],[577,5194,5195],{"xmlns":579},[581,5196,5197,5210],{},[584,5198,5199,5205,5207],{},[1744,5200,5201,5203],{},[587,5202,2286],{},[804,5204,1826],{},[738,5206,3328],{},[804,5208,5209],{},"3,04",[591,5211,5212],{"encoding":593},"c_2 \\approx 3{,}04",[568,5214,5216,5271],{"className":5215,"ariaHidden":598},[597],[568,5217,5219,5222,5262,5265,5268],{"className":5218},[602],[568,5220],{"className":5221,"style":5117},[606],[568,5223,5225,5228],{"className":5224},[611],[568,5226,2286],{"className":5227},[611,612],[568,5229,5231],{"className":5230},[878],[568,5232,5234,5254],{"className":5233},[882,1774],[568,5235,5237,5251],{"className":5236},[886],[568,5238,5240],{"className":5239,"style":1781},[890],[568,5241,5242,5245],{"style":5138},[568,5243],{"className":5244,"style":899},[898],[568,5246,5248],{"className":5247},[903,904,905,906],[568,5249,1826],{"className":5250},[611,906],[568,5252,1798],{"className":5253},[1797],[568,5255,5257],{"className":5256},[886],[568,5258,5260],{"className":5259,"style":1805},[890],[568,5261],{},[568,5263],{"className":5264,"style":842},[764],[568,5266,3328],{"className":5267},[846],[568,5269],{"className":5270,"style":842},[764],[568,5272,5274,5277,5281,5287],{"className":5273},[602],[568,5275],{"className":5276,"style":3510},[606],[568,5278,5280],{"className":5279},[611],"3",[568,5282,5284],{"className":5283},[611],[568,5285,3521],{"className":5286},[3520],[568,5288,5290],{"className":5289},[611],"04",". Beide Dreiecke existieren.",[564,5293,5294,3042,5297,613,5348,613,5398,5481,5482,5734,5735,5763],{},[678,5295,5296],{},"Keine Lösung:",[568,5298,5300,5318],{"className":5299},[571],[568,5301,5303],{"className":5302},[575],[577,5304,5305],{"xmlns":579},[581,5306,5307,5315],{},[584,5308,5309,5311,5313],{},[587,5310,589],{},[738,5312,791],{},[804,5314,5280],{},[591,5316,5317],{"encoding":593},"a = 3",[568,5319,5321,5339],{"className":5320,"ariaHidden":598},[597],[568,5322,5324,5327,5330,5333,5336],{"className":5323},[602],[568,5325],{"className":5326,"style":607},[606],[568,5328,589],{"className":5329},[611,612],[568,5331],{"className":5332,"style":842},[764],[568,5334,791],{"className":5335},[846],[568,5337],{"className":5338,"style":842},[764],[568,5340,5342,5345],{"className":5341},[602],[568,5343],{"className":5344,"style":1495},[606],[568,5346,5280],{"className":5347},[611],[568,5349,5351,5368],{"className":5350},[571],[568,5352,5354],{"className":5353},[575],[577,5355,5356],{"xmlns":579},[581,5357,5358,5366],{},[584,5359,5360,5362,5364],{},[587,5361,628],{},[738,5363,791],{},[804,5365,3061],{},[591,5367,4115],{"encoding":593},[568,5369,5371,5389],{"className":5370,"ariaHidden":598},[597],[568,5372,5374,5377,5380,5383,5386],{"className":5373},[602],[568,5375],{"className":5376,"style":640},[606],[568,5378,628],{"className":5379},[611,612],[568,5381],{"className":5382,"style":842},[764],[568,5384,791],{"className":5385},[846],[568,5387],{"className":5388,"style":842},[764],[568,5390,5392,5395],{"className":5391},[602],[568,5393],{"className":5394,"style":1495},[606],[568,5396,3061],{"className":5397},[611],[568,5399,5401,5422],{"className":5400},[571],[568,5402,5404],{"className":5403},[575],[577,5405,5406],{"xmlns":579},[581,5407,5408,5420],{},[584,5409,5410,5412,5414],{},[587,5411,659],{},[738,5413,791],{},[801,5415,5416,5418],{},[804,5417,4166],{},[738,5419,809],{},[591,5421,4171],{"encoding":593},[568,5423,5425,5443],{"className":5424,"ariaHidden":598},[597],[568,5426,5428,5431,5434,5437,5440],{"className":5427},[602],[568,5429],{"className":5430,"style":607},[606],[568,5432,659],{"className":5433,"style":675},[611,612],[568,5435],{"className":5436,"style":842},[764],[568,5438,791],{"className":5439},[846],[568,5441],{"className":5442,"style":842},[764],[568,5444,5446,5449,5452],{"className":5445},[602],[568,5447],{"className":5448,"style":891},[606],[568,5450,3682],{"className":5451},[611],[568,5453,5455,5458],{"className":5454},[611],[568,5456,874],{"className":5457},[611],[568,5459,5461],{"className":5460},[878],[568,5462,5464],{"className":5463},[882],[568,5465,5467],{"className":5466},[886],[568,5468,5470],{"className":5469,"style":891},[890],[568,5471,5472,5475],{"style":894},[568,5473],{"className":5474,"style":899},[898],[568,5476,5478],{"className":5477},[903,904,905,906],[568,5479,809],{"className":5480},[910,906],". Dann wäre ",[568,5483,5485,5532],{"className":5484},[571],[568,5486,5488],{"className":5487},[575],[577,5489,5490],{"xmlns":579},[581,5491,5492,5529],{},[584,5493,5494,5496,5498,5500,5502,5520,5522,5525,5527],{},[587,5495,736],{},[738,5497,740],{},[587,5499,743],{},[738,5501,791],{},[2290,5503,5504,5518],{},[584,5505,5506,5508,5510,5512],{},[804,5507,3061],{},[587,5509,736],{},[738,5511,740],{},[801,5513,5514,5516],{},[804,5515,4166],{},[738,5517,809],{},[804,5519,5280],{},[738,5521,3328],{},[804,5523,5524],{},"1,71",[738,5526,957],{},[804,5528,1458],{},[591,5530,5531],{"encoding":593},"\\sin \\beta = \\frac{8 \\sin 40^\\circ}{3} \\approx 1{,}71 > 1",[568,5533,5535,5559,5697,5725],{"className":5534,"ariaHidden":598},[597],[568,5536,5538,5541,5544,5547,5550,5553,5556],{"className":5537},[602],[568,5539],{"className":5540,"style":756},[606],[568,5542,736],{"className":5543},[760],[568,5545],{"className":5546,"style":765},[764],[568,5548,743],{"className":5549,"style":769},[611,612],[568,5551],{"className":5552,"style":842},[764],[568,5554,791],{"className":5555},[846],[568,5557],{"className":5558,"style":842},[764],[568,5560,5562,5566,5688,5691,5694],{"className":5561},[602],[568,5563],{"className":5564,"style":5565},[606],"height:1.2629em;vertical-align:-0.345em;",[568,5567,5569,5572,5685],{"className":5568},[611],[568,5570],{"className":5571},[863,2347],[568,5573,5575],{"className":5574},[2290],[568,5576,5578,5677],{"className":5577},[882,1774],[568,5579,5581,5674],{"className":5580},[886],[568,5582,5585,5599,5607],{"className":5583,"style":5584},[890],"height:0.9179em;",[568,5586,5587,5590],{"style":2363},[568,5588],{"className":5589,"style":2367},[898],[568,5591,5593],{"className":5592},[903,904,905,906],[568,5594,5596],{"className":5595},[611,906],[568,5597,5280],{"className":5598},[611,906],[568,5600,5601,5604],{"style":2398},[568,5602],{"className":5603,"style":2367},[898],[568,5605],{"className":5606,"style":2406},[2405],[568,5608,5610,5613],{"style":5609},"top:-3.394em;",[568,5611],{"className":5612,"style":2367},[898],[568,5614,5616],{"className":5615},[903,904,905,906],[568,5617,5619,5622,5625,5637,5640,5643],{"className":5618},[611,906],[568,5620,3061],{"className":5621},[611,906],[568,5623],{"className":5624,"style":2392},[764,906],[568,5626,5628,5631,5634],{"className":5627},[760,906],[568,5629,2380],{"className":5630},[906],[568,5632,2384],{"className":5633},[906],[568,5635,2388],{"className":5636},[906],[568,5638],{"className":5639,"style":2392},[764,906],[568,5641,3682],{"className":5642},[611,906],[568,5644,5646,5649],{"className":5645},[611,906],[568,5647,874],{"className":5648},[611,906],[568,5650,5652],{"className":5651},[878],[568,5653,5655],{"className":5654},[882],[568,5656,5658],{"className":5657},[886],[568,5659,5662],{"className":5660,"style":5661},[890],"height:0.7485em;",[568,5663,5665,5668],{"style":5664},"top:-2.931em;margin-right:0.0714em;",[568,5666],{"className":5667,"style":3853},[898],[568,5669,5671],{"className":5670},[903,3857,3858,906],[568,5672,809],{"className":5673},[910,906],[568,5675,1798],{"className":5676},[1797],[568,5678,5680],{"className":5679},[886],[568,5681,5683],{"className":5682,"style":2452},[890],[568,5684],{},[568,5686],{"className":5687},[933,2347],[568,5689],{"className":5690,"style":842},[764],[568,5692,3328],{"className":5693},[846],[568,5695],{"className":5696,"style":842},[764],[568,5698,5700,5703,5706,5712,5716,5719,5722],{"className":5699},[602],[568,5701],{"className":5702,"style":3510},[606],[568,5704,1458],{"className":5705},[611],[568,5707,5709],{"className":5708},[611],[568,5710,3521],{"className":5711},[3520],[568,5713,5715],{"className":5714},[611],"71",[568,5717],{"className":5718,"style":842},[764],[568,5720,957],{"className":5721},[846],[568,5723],{"className":5724,"style":842},[764],[568,5726,5728,5731],{"className":5727},[602],[568,5729],{"className":5730,"style":1495},[606],[568,5732,1458],{"className":5733},[611],". Die Seite ",[568,5736,5738,5751],{"className":5737},[571],[568,5739,5741],{"className":5740},[575],[577,5742,5743],{"xmlns":579},[581,5744,5745,5749],{},[584,5746,5747],{},[587,5748,589],{},[591,5750,589],{"encoding":593},[568,5752,5754],{"className":5753,"ariaHidden":598},[597],[568,5755,5757,5760],{"className":5756},[602],[568,5758],{"className":5759,"style":607},[606],[568,5761,589],{"className":5762},[611,612]," ist zu kurz, um die dritte Seite zu erreichen.",[559,5765,5767],{"id":5766},"typische-fehler","Typische Fehler",[936,5769,5770,5969,6241],{},[939,5771,5772,5773,5842,5843,5968],{},"Nur den Taschenrechnerwert ",[568,5774,5776,5793],{"className":5775},[571],[568,5777,5779],{"className":5778},[575],[577,5780,5781],{"xmlns":579},[581,5782,5783,5791],{},[584,5784,5785],{},[1744,5786,5787,5789],{},[587,5788,743],{},[804,5790,1458],{},[591,5792,1752],{"encoding":593},[568,5794,5796],{"className":5795,"ariaHidden":598},[597],[568,5797,5799,5802],{"className":5798},[602],[568,5800],{"className":5801,"style":756},[606],[568,5803,5805,5808],{"className":5804},[611],[568,5806,743],{"className":5807,"style":769},[611,612],[568,5809,5811],{"className":5810},[878],[568,5812,5814,5834],{"className":5813},[882,1774],[568,5815,5817,5831],{"className":5816},[886],[568,5818,5820],{"className":5819,"style":1781},[890],[568,5821,5822,5825],{"style":1784},[568,5823],{"className":5824,"style":899},[898],[568,5826,5828],{"className":5827},[903,904,905,906],[568,5829,1458],{"className":5830},[611,906],[568,5832,1798],{"className":5833},[1797],[568,5835,5837],{"className":5836},[886],[568,5838,5840],{"className":5839,"style":1805},[890],[568,5841],{}," nehmen und die zweite Lösung ",[568,5844,5846,5872],{"className":5845},[571],[568,5847,5849],{"className":5848},[575],[577,5850,5851],{"xmlns":579},[581,5852,5853,5869],{},[584,5854,5855,5861,5863],{},[801,5856,5857,5859],{},[804,5858,806],{},[738,5860,809],{},[738,5862,812],{},[1744,5864,5865,5867],{},[587,5866,743],{},[804,5868,1458],{},[591,5870,5871],{"encoding":593},"180^\\circ - \\beta_1",[568,5873,5875,5922],{"className":5874,"ariaHidden":598},[597],[568,5876,5878,5881,5884,5913,5916,5919],{"className":5877},[602],[568,5879],{"className":5880,"style":1910},[606],[568,5882,867],{"className":5883},[611],[568,5885,5887,5890],{"className":5886},[611],[568,5888,874],{"className":5889},[611],[568,5891,5893],{"className":5892},[878],[568,5894,5896],{"className":5895},[882],[568,5897,5899],{"className":5898},[886],[568,5900,5902],{"className":5901,"style":891},[890],[568,5903,5904,5907],{"style":894},[568,5905],{"className":5906,"style":899},[898],[568,5908,5910],{"className":5909},[903,904,905,906],[568,5911,809],{"className":5912},[910,906],[568,5914],{"className":5915,"style":914},[764],[568,5917,812],{"className":5918},[910],[568,5920],{"className":5921,"style":914},[764],[568,5923,5925,5928],{"className":5924},[602],[568,5926],{"className":5927,"style":756},[606],[568,5929,5931,5934],{"className":5930},[611],[568,5932,743],{"className":5933,"style":769},[611,612],[568,5935,5937],{"className":5936},[878],[568,5938,5940,5960],{"className":5939},[882,1774],[568,5941,5943,5957],{"className":5942},[886],[568,5944,5946],{"className":5945,"style":1781},[890],[568,5947,5948,5951],{"style":1784},[568,5949],{"className":5950,"style":899},[898],[568,5952,5954],{"className":5953},[903,904,905,906],[568,5955,1458],{"className":5956},[611,906],[568,5958,1798],{"className":5959},[1797],[568,5961,5963],{"className":5962},[886],[568,5964,5966],{"className":5965,"style":1805},[890],[568,5967],{}," übersehen.",[939,5970,5971,5972,6023,6024,6148,6149,6177,6178,6240],{},"Die zweite Lösung ungeprüft übernehmen. Bei ",[568,5973,5975,5993],{"className":5974},[571],[568,5976,5978],{"className":5977},[575],[577,5979,5980],{"xmlns":579},[581,5981,5982,5990],{},[584,5983,5984,5986,5988],{},[587,5985,589],{},[738,5987,2066],{},[587,5989,628],{},[591,5991,5992],{"encoding":593},"a \\ge b",[568,5994,5996,6014],{"className":5995,"ariaHidden":598},[597],[568,5997,5999,6002,6005,6008,6011],{"className":5998},[602],[568,6000],{"className":6001,"style":2085},[606],[568,6003,589],{"className":6004},[611,612],[568,6006],{"className":6007,"style":842},[764],[568,6009,2066],{"className":6010},[846],[568,6012],{"className":6013,"style":842},[764],[568,6015,6017,6020],{"className":6016},[602],[568,6018],{"className":6019,"style":640},[606],[568,6021,628],{"className":6022},[611,612]," ergibt ",[568,6025,6027,6052],{"className":6026},[571],[568,6028,6030],{"className":6029},[575],[577,6031,6032],{"xmlns":579},[581,6033,6034,6050],{},[584,6035,6036,6042,6044],{},[801,6037,6038,6040],{},[804,6039,806],{},[738,6041,809],{},[738,6043,812],{},[1744,6045,6046,6048],{},[587,6047,743],{},[804,6049,1458],{},[591,6051,5871],{"encoding":593},[568,6053,6055,6102],{"className":6054,"ariaHidden":598},[597],[568,6056,6058,6061,6064,6093,6096,6099],{"className":6057},[602],[568,6059],{"className":6060,"style":1910},[606],[568,6062,867],{"className":6063},[611],[568,6065,6067,6070],{"className":6066},[611],[568,6068,874],{"className":6069},[611],[568,6071,6073],{"className":6072},[878],[568,6074,6076],{"className":6075},[882],[568,6077,6079],{"className":6078},[886],[568,6080,6082],{"className":6081,"style":891},[890],[568,6083,6084,6087],{"style":894},[568,6085],{"className":6086,"style":899},[898],[568,6088,6090],{"className":6089},[903,904,905,906],[568,6091,809],{"className":6092},[910,906],[568,6094],{"className":6095,"style":914},[764],[568,6097,812],{"className":6098},[910],[568,6100],{"className":6101,"style":914},[764],[568,6103,6105,6108],{"className":6104},[602],[568,6106],{"className":6107,"style":756},[606],[568,6109,6111,6114],{"className":6110},[611],[568,6112,743],{"className":6113,"style":769},[611,612],[568,6115,6117],{"className":6116},[878],[568,6118,6120,6140],{"className":6119},[882,1774],[568,6121,6123,6137],{"className":6122},[886],[568,6124,6126],{"className":6125,"style":1781},[890],[568,6127,6128,6131],{"style":1784},[568,6129],{"className":6130,"style":899},[898],[568,6132,6134],{"className":6133},[903,904,905,906],[568,6135,1458],{"className":6136},[611,906],[568,6138,1798],{"className":6139},[1797],[568,6141,6143],{"className":6142},[886],[568,6144,6146],{"className":6145,"style":1805},[890],[568,6147],{}," zusammen mit ",[568,6150,6152,6165],{"className":6151},[571],[568,6153,6155],{"className":6154},[575],[577,6156,6157],{"xmlns":579},[581,6158,6159,6163],{},[584,6160,6161],{},[587,6162,659],{},[591,6164,662],{"encoding":593},[568,6166,6168],{"className":6167,"ariaHidden":598},[597],[568,6169,6171,6174],{"className":6170},[602],[568,6172],{"className":6173,"style":607},[606],[568,6175,659],{"className":6176,"style":675},[611,612]," mindestens ",[568,6179,6181,6199],{"className":6180},[571],[568,6182,6184],{"className":6183},[575],[577,6185,6186],{"xmlns":579},[581,6187,6188,6196],{},[584,6189,6190],{},[801,6191,6192,6194],{},[804,6193,806],{},[738,6195,809],{},[591,6197,6198],{"encoding":593},"180^\\circ",[568,6200,6202],{"className":6201,"ariaHidden":598},[597],[568,6203,6205,6208,6211],{"className":6204},[602],[568,6206],{"className":6207,"style":891},[606],[568,6209,867],{"className":6210},[611],[568,6212,6214,6217],{"className":6213},[611],[568,6215,874],{"className":6216},[611],[568,6218,6220],{"className":6219},[878],[568,6221,6223],{"className":6222},[882],[568,6224,6226],{"className":6225},[886],[568,6227,6229],{"className":6228,"style":891},[890],[568,6230,6231,6234],{"style":894},[568,6232],{"className":6233,"style":899},[898],[568,6235,6237],{"className":6236},[903,904,905,906],[568,6238,809],{"className":6239},[910,906]," und ist kein Dreieck.",[939,6242,6243,6244,6272,6273,6301],{},"Den Winkel der falschen Seite zuordnen: ",[568,6245,6247,6260],{"className":6246},[571],[568,6248,6250],{"className":6249},[575],[577,6251,6252],{"xmlns":579},[581,6253,6254,6258],{},[584,6255,6256],{},[587,6257,659],{},[591,6259,662],{"encoding":593},[568,6261,6263],{"className":6262,"ariaHidden":598},[597],[568,6264,6266,6269],{"className":6265},[602],[568,6267],{"className":6268,"style":607},[606],[568,6270,659],{"className":6271,"style":675},[611,612]," muss der Seite ",[568,6274,6276,6289],{"className":6275},[571],[568,6277,6279],{"className":6278},[575],[577,6280,6281],{"xmlns":579},[581,6282,6283,6287],{},[584,6284,6285],{},[587,6286,589],{},[591,6288,589],{"encoding":593},[568,6290,6292],{"className":6291,"ariaHidden":598},[597],[568,6293,6295,6298],{"className":6294},[602],[568,6296],{"className":6297,"style":607},[606],[568,6299,589],{"className":6300},[611,612]," 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