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Sinussatz hilft, wenn eine Seite und ihr gegenüberliegender Winkel bekannt sind, dazu eine weitere Seite oder ein weiterer Winkel. Den dritten Winkel liefert die Winkelsumme ",[577,1395,1397,1432],{"className":1396},[580],[577,1398,1400],{"className":1399},[584],[586,1401,1402],{"xmlns":588},[590,1403,1404,1429],{},[593,1405,1406,1408,1411,1413,1415,1417,1419],{},[596,1407,698],{},[1017,1409,1410],{},"+",[596,1412,730],{},[1017,1414,1410],{},[596,1416,762],{},[1017,1418,1024],{},[1420,1421,1422,1426],"msup",{},[1423,1424,1425],"mn",{},"180",[1017,1427,1428],{},"∘",[600,1430,1431],{"encoding":602},"\\alpha + \\beta + \\gamma = 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5\\,\\text{cm}",[577,1575,1577,1595],{"className":1576,"ariaHidden":607},[606],[577,1578,1580,1583,1586,1589,1592],{"className":1579},[611],[577,1581],{"className":1582,"style":711},[615],[577,1584,795],{"className":1585},[620,621],[577,1587],{"className":1588,"style":1177},[1038],[577,1590,1024],{"className":1591},[1181],[577,1593],{"className":1594,"style":1177},[1038],[577,1596,1598,1602,1605,1608],{"className":1597},[611],[577,1599],{"className":1600,"style":1601},[615],"height:0.6444em;",[577,1603,1563],{"className":1604},[620],[577,1606],{"className":1607,"style":1129},[1038],[577,1609,1612],{"className":1610},[620,1611],"text",[577,1613,1570],{"className":1614},[620],[577,1616,1618,1641],{"className":1617},[580],[577,1619,1621],{"className":1620},[584],[586,1622,1623],{"xmlns":588},[590,1624,1625,1638],{},[593,1626,1627,1629,1631],{},[596,1628,698],{},[1017,1630,1024],{},[1420,1632,1633,1636],{},[1423,1634,1635],{},"40",[1017,1637,1428],{},[600,1639,1640],{"encoding":602},"\\alpha = 40^\\circ",[577,1642,1644,1662],{"className":1643,"ariaHidden":607},[606],[577,1645,1647,1650,1653,1656,1659],{"className":1646},[611],[577,1648],{"className":1649,"style":711},[615],[577,1651,698],{"className":1652,"style":715},[620,621],[577,1654],{"className":1655,"style":1177},[1038],[577,1657,1024],{"className":1658},[1181],[577,1660],{"className":1661,"style":1177},[1038],[577,1663,1665,1668,1672],{"className":1664},[611],[577,1666],{"className":1667,"style":1496},[615],[577,1669,1671],{"className":1670},[620],"4",[577,1673,1675,1678],{"className":1674},[620],[577,1676,1507],{"className":1677},[620],[577,1679,1681],{"className":1680},[1511],[577,1682,1684],{"className":1683},[1100],[577,1685,1687],{"className":1686},[1105],[577,1688,1690],{"className":1689,"style":1496},[1109],[577,1691,1692,1695],{"style":1523},[577,1693],{"className":1694,"style":1527},[1117],[577,1696,1698],{"className":1697},[1531,1532,1533,1534],[577,1699,1428],{"className":1700},[1364,1534],[577,1702,1704,1727],{"className":1703},[580],[577,1705,1707],{"className":1706},[584],[586,1708,1709],{"xmlns":588},[590,1710,1711,1724],{},[593,1712,1713,1715,1717],{},[596,1714,730],{},[1017,1716,1024],{},[1420,1718,1719,1722],{},[1423,1720,1721],{},"60",[1017,1723,1428],{},[600,1725,1726],{"encoding":602},"\\beta 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Gesucht sind 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= \\frac{5\\,\\text{cm} \\cdot \\sin 60^\\circ}{\\sin 40^\\circ} \\approx 6{,}74\\,\\text{cm}",[577,1912,1914,1932,2104],{"className":1913,"ariaHidden":607},[606],[577,1915,1917,1920,1923,1926,1929],{"className":1916},[611],[577,1918],{"className":1919,"style":895},[615],[577,1921,883],{"className":1922},[620,621],[577,1924],{"className":1925,"style":1177},[1038],[577,1927,1024],{"className":1928},[1181],[577,1930],{"className":1931,"style":1177},[1038],[577,1933,1935,1939,2095,2098,2101],{"className":1934},[611],[577,1936],{"className":1937,"style":1938},[615],"height:2.0371em;vertical-align:-0.686em;",[577,1940,1942,1945,2092],{"className":1941},[620],[577,1943],{"className":1944},[1092,1093],[577,1946,1948],{"className":1947},[1007],[577,1949,1951,2084],{"className":1950},[1100,1101],[577,1952,1954,2081],{"className":1953},[1105],[577,1955,1958,2006,2014],{"className":1956,"style":1957},[1109],"height:1.3511em;",[577,1959,1960,1963],{"style":1113},[577,1961],{"className":1962,"style":1118},[1117],[577,1964,1966,1969,1972,1975],{"className":1965},[620],[577,1967,1015],{"className":1968},[1125],[577,1970],{"className":1971,"style":1129},[1038],[577,1973,1671],{"className":1974},[620],[577,1976,1978,1981],{"className":1977},[620],[577,1979,1507],{"className":1980},[620],[577,1982,1984],{"className":1983},[1511],[577,1985,1987],{"className":1986},[1100],[577,1988,1990],{"className":1989},[1105],[577,1991,1994],{"className":1992,"style":1993},[1109],"height:0.6001em;",[577,1995,1997,2000],{"style":1996},"top:-2.989em;margin-right:0.05em;",[577,1998],{"className":1999,"style":1527},[1117],[577,2001,2003],{"className":2002},[1531,1532,1533,1534],[577,2004,1428],{"className":2005},[1364,1534],[577,2007,2008,2011],{"style":1135},[577,2009],{"className":2010,"style":1118},[1117],[577,2012],{"className":2013,"style":1143},[1142],[577,2015,2016,2019],{"style":1146},[577,2017],{"className":2018,"style":1118},[1117],[577,2020,2022,2025,2028,2034,2037,2040,2043,2046,2049,2052],{"className":2021},[620],[577,2023,1563],{"className":2024},[620],[577,2026],{"className":2027,"style":1129},[1038],[577,2029,2031],{"className":2030},[620,1611],[577,2032,1570],{"className":2033},[620],[577,2035],{"className":2036,"style":1360},[1038],[577,2038,1058],{"className":2039},[1364],[577,2041],{"className":2042,"style":1360},[1038],[577,2044,1015],{"className":2045},[1125],[577,2047],{"className":2048,"style":1129},[1038],[577,2050,1757],{"className":2051},[620],[577,2053,2055,2058],{"className":2054},[620],[577,2056,1507],{"className":2057},[620],[577,2059,2061],{"className":2060},[1511],[577,2062,2064],{"className":2063},[1100],[577,2065,2067],{"className":2066},[1105],[577,2068,2070],{"className":2069,"style":1496},[1109],[577,2071,2072,2075],{"style":1523},[577,2073],{"className":2074,"style":1527},[1117],[577,2076,2078],{"className":2077},[1531,1532,1533,1534],[577,2079,1428],{"className":2080},[1364,1534],[577,2082,1160],{"className":2083},[1159],[577,2085,2087],{"className":2086},[1105],[577,2088,2090],{"className":2089,"style":1167},[1109],[577,2091],{},[577,2093],{"className":2094},[1173,1093],[577,2096],{"className":2097,"style":1177},[1038],[577,2099,1900],{"className":2100},[1181],[577,2102],{"className":2103,"style":1177},[1038],[577,2105,2107,2111,2114,2122,2126,2129],{"className":2106},[611],[577,2108],{"className":2109,"style":2110},[615],"height:0.8389em;vertical-align:-0.1944em;",[577,2112,1757],{"className":2113},[620],[577,2115,2117],{"className":2116},[620],[577,2118,2121],{"className":2119},[2120],"mpunct",",",[577,2123,2125],{"className":2124},[620],"74",[577,2127],{"className":2128,"style":1129},[1038],[577,2130,2132],{"className":2131},[620,1611],[577,2133,1570],{"className":2134},[620],[564,2136,2137,2138,1844],{},"Mit ",[577,2139,2141,2189],{"className":2140},[580],[577,2142,2144],{"className":2143},[584],[586,2145,2146],{"xmlns":588},[590,2147,2148,2186],{},[593,2149,2150,2152,2154,2160,2163,2169,2171,2177,2179],{},[596,2151,762],{},[1017,2153,1024],{},[1420,2155,2156,2158],{},[1423,2157,1425],{},[1017,2159,1428],{},[1017,2161,2162],{},"−",[1420,2164,2165,2167],{},[1423,2166,1635],{},[1017,2168,1428],{},[1017,2170,2162],{},[1420,2172,2173,2175],{},[1423,2174,1721],{},[1017,2176,1428],{},[1017,2178,1024],{},[1420,2180,2181,2184],{},[1423,2182,2183],{},"80",[1017,2185,1428],{},[600,2187,2188],{"encoding":602},"\\gamma = 180^\\circ - 40^\\circ - 60^\\circ = 80^\\circ",[577,2190,2192,2210,2258,2305,2352],{"className":2191,"ariaHidden":607},[606],[577,2193,2195,2198,2201,2204,2207],{"className":2194},[611],[577,2196],{"className":2197,"style":775},[615],[577,2199,762],{"className":2200,"style":779},[620,621],[577,2202],{"className":2203,"style":1177},[1038],[577,2205,1024],{"className":2206},[1181],[577,2208],{"className":2209,"style":1177},[1038],[577,2211,2213,2217,2220,2249,2252,2255],{"className":2212},[611],[577,2214],{"className":2215,"style":2216},[615],"height:0.7574em;vertical-align:-0.0833em;",[577,2218,1500],{"className":2219},[620],[577,2221,2223,2226],{"className":2222},[620],[577,2224,1507],{"className":2225},[620],[577,2227,2229],{"className":2228},[1511],[577,2230,2232],{"className":2231},[1100],[577,2233,2235],{"className":2234},[1105],[577,2236,2238],{"className":2237,"style":1496},[1109],[577,2239,2240,2243],{"style":1523},[577,2241],{"className":2242,"style":1527},[1117],[577,2244,2246],{"className":2245},[1531,1532,1533,1534],[577,2247,1428],{"className":2248},[1364,1534],[577,2250],{"className":2251,"style":1360},[1038],[577,2253,2162],{"className":2254},[1364],[577,2256],{"className":2257,"style":1360},[1038],[577,2259,2261,2264,2267,2296,2299,2302],{"className":2260},[611],[577,2262],{"className":2263,"style":2216},[615],[577,2265,1671],{"className":2266},[620],[577,2268,2270,2273],{"className":2269},[620],[577,2271,1507],{"className":2272},[620],[577,2274,2276],{"className":2275},[1511],[577,2277,2279],{"className":2278},[1100],[577,2280,2282],{"className":2281},[1105],[577,2283,2285],{"className":2284,"style":1496},[1109],[577,2286,2287,2290],{"style":1523},[577,2288],{"className":2289,"style":1527},[1117],[577,2291,2293],{"className":2292},[1531,1532,1533,1534],[577,2294,1428],{"className":2295},[1364,1534],[577,2297],{"className":2298,"style":1360},[1038],[577,2300,2162],{"className":2301},[1364],[577,2303],{"className":2304,"style":1360},[1038],[577,2306,2308,2311,2314,2343,2346,2349],{"className":2307},[611],[577,2309],{"className":2310,"style":1496},[615],[577,2312,1757],{"className":2313},[620],[577,2315,2317,2320],{"className":2316},[620],[577,2318,1507],{"className":2319},[620],[577,2321,2323],{"className":2322},[1511],[577,2324,2326],{"className":2325},[1100],[577,2327,2329],{"className":2328},[1105],[577,2330,2332],{"className":2331,"style":1496},[1109],[577,2333,2334,2337],{"style":1523},[577,2335],{"className":2336,"style":1527},[1117],[577,2338,2340],{"className":2339},[1531,1532,1533,1534],[577,2341,1428],{"className":2342},[1364,1534],[577,2344],{"className":2345,"style":1177},[1038],[577,2347,1024],{"className":2348},[1181],[577,2350],{"className":2351,"style":1177},[1038],[577,2353,2355,2358,2362],{"className":2354},[611],[577,2356],{"className":2357,"style":1496},[615],[577,2359,2361],{"className":2360},[620],"8",[577,2363,2365,2368],{"className":2364},[620],[577,2366,1507],{"className":2367},[620],[577,2369,2371],{"className":2370},[1511],[577,2372,2374],{"className":2373},[1100],[577,2375,2377],{"className":2376},[1105],[577,2378,2380],{"className":2379,"style":1496},[1109],[577,2381,2382,2385],{"style":1523},[577,2383],{"className":2384,"style":1527},[1117],[577,2386,2388],{"className":2387},[1531,1532,1533,1534],[577,2389,1428],{"className":2390},[1364,1534],[577,2392,2394],{"className":2393},[992],[577,2395,2397,2456],{"className":2396},[580],[577,2398,2400],{"className":2399},[584],[586,2401,2402],{"xmlns":588,"display":1001},[590,2403,2404,2453],{},[593,2405,2406,2408,2410,2444,2446,2449,2451],{},[596,2407,942],{},[1017,2409,1024],{},[1007,2411,2412,2432],{},[593,2413,2414,2416,2418,2420,2422,2424,2426],{},[1423,2415,1563],{},[1565,2417,1567],{},[1565,2419,1570],{},[1017,2421,1058],{},[596,2423,1015],{},[1017,2425,1019],{},[1420,2427,2428,2430],{},[1423,2429,2183],{},[1017,2431,1428],{},[593,2433,2434,2436,2438],{},[596,2435,1015],{},[1017,2437,1019],{},[1420,2439,2440,2442],{},[1423,2441,1635],{},[1017,2443,1428],{},[1017,2445,1900],{},[1423,2447,2448],{},"7,66",[1565,2450,1567],{},[1565,2452,1570],{},[600,2454,2455],{"encoding":602},"c = \\frac{5\\,\\text{cm} \\cdot \\sin 80^\\circ}{\\sin 40^\\circ} \\approx 7{,}66\\,\\text{cm}",[577,2457,2459,2477,2645],{"className":2458,"ariaHidden":607},[606],[577,2460,2462,2465,2468,2471,2474],{"className":2461},[611],[577,2463],{"className":2464,"style":711},[615],[577,2466,942],{"className":2467},[620,621],[577,2469],{"className":2470,"style":1177},[1038],[577,2472,1024],{"className":2473},[1181],[577,2475],{"className":2476,"style":1177},[1038],[577,2478,2480,2483,2636,2639,2642],{"className":2479},[611],[577,2481],{"className":2482,"style":1938},[615],[577,2484,2486,2489,2633],{"className":2485},[620],[577,2487],{"className":2488},[1092,1093],[577,2490,2492],{"className":2491},[1007],[577,2493,2495,2625],{"className":2494},[1100,1101],[577,2496,2498,2622],{"className":2497},[1105],[577,2499,2501,2547,2555],{"className":2500,"style":1957},[1109],[577,2502,2503,2506],{"style":1113},[577,2504],{"className":2505,"style":1118},[1117],[577,2507,2509,2512,2515,2518],{"className":2508},[620],[577,2510,1015],{"className":2511},[1125],[577,2513],{"className":2514,"style":1129},[1038],[577,2516,1671],{"className":2517},[620],[577,2519,2521,2524],{"className":2520},[620],[577,2522,1507],{"className":2523},[620],[577,2525,2527],{"className":2526},[1511],[577,2528,2530],{"className":2529},[1100],[577,2531,2533],{"className":2532},[1105],[577,2534,2536],{"className":2535,"style":1993},[1109],[577,2537,2538,2541],{"style":1996},[577,2539],{"className":2540,"style":1527},[1117],[577,2542,2544],{"className":2543},[1531,1532,1533,1534],[577,2545,1428],{"className":2546},[1364,1534],[577,2548,2549,2552],{"style":1135},[577,2550],{"className":2551,"style":1118},[1117],[577,2553],{"className":2554,"style":1143},[1142],[577,2556,2557,2560],{"style":1146},[577,2558],{"className":2559,"style":1118},[1117],[577,2561,2563,2566,2569,2575,2578,2581,2584,2587,2590,2593],{"className":2562},[620],[577,2564,1563],{"className":2565},[620],[577,2567],{"className":2568,"style":1129},[1038],[577,2570,2572],{"className":2571},[620,1611],[577,2573,1570],{"className":2574},[620],[577,2576],{"className":2577,"style":1360},[1038],[577,2579,1058],{"className":2580},[1364],[577,2582],{"className":2583,"style":1360},[1038],[577,2585,1015],{"className":2586},[1125],[577,2588],{"className":2589,"style":1129},[1038],[577,2591,2361],{"className":2592},[620],[577,2594,2596,2599],{"className":2595},[620],[577,2597,1507],{"className":2598},[620],[577,2600,2602],{"className":2601},[1511],[577,2603,2605],{"className":2604},[1100],[577,2606,2608],{"className":2607},[1105],[577,2609,2611],{"className":2610,"style":1496},[1109],[577,2612,2613,2616],{"style":1523},[577,2614],{"className":2615,"style":1527},[1117],[577,2617,2619],{"className":2618},[1531,1532,1533,1534],[577,2620,1428],{"className":2621},[1364,1534],[577,2623,1160],{"className":2624},[1159],[577,2626,2628],{"className":2627},[1105],[577,2629,2631],{"className":2630,"style":1167},[1109],[577,2632],{},[577,2634],{"className":2635},[1173,1093],[577,2637],{"className":2638,"style":1177},[1038],[577,2640,1900],{"className":2641},[1181],[577,2643],{"className":2644,"style":1177},[1038],[577,2646,2648,2651,2655,2661,2665,2668],{"className":2647},[611],[577,2649],{"className":2650,"style":2110},[615],[577,2652,2654],{"className":2653},[620],"7",[577,2656,2658],{"className":2657},[620],[577,2659,2121],{"className":2660},[2120],[577,2662,2664],{"className":2663},[620],"66",[577,2666],{"className":2667,"style":1129},[1038],[577,2669,2671],{"className":2670},[620,1611],[577,2672,1570],{"className":2673},[620],[564,2675,1544,2676,622,2740,899,2804,2889,2890,1844],{},[577,2677,2679,2701],{"className":2678},[580],[577,2680,2682],{"className":2681},[584],[586,2683,2684],{"xmlns":588},[590,2685,2686,2698],{},[593,2687,2688,2690,2692,2694,2696],{},[596,2689,795],{},[1017,2691,1024],{},[1423,2693,2361],{},[1565,2695,1567],{},[1565,2697,1570],{},[600,2699,2700],{"encoding":602},"a = 8\\,\\text{cm}",[577,2702,2704,2722],{"className":2703,"ariaHidden":607},[606],[577,2705,2707,2710,2713,2716,2719],{"className":2706},[611],[577,2708],{"className":2709,"style":711},[615],[577,2711,795],{"className":2712},[620,621],[577,2714],{"className":2715,"style":1177},[1038],[577,2717,1024],{"className":2718},[1181],[577,2720],{"className":2721,"style":1177},[1038],[577,2723,2725,2728,2731,2734],{"className":2724},[611],[577,2726],{"className":2727,"style":1601},[615],[577,2729,2361],{"className":2730},[620],[577,2732],{"className":2733,"style":1129},[1038],[577,2735,2737],{"className":2736},[620,1611],[577,2738,1570],{"className":2739},[620],[577,2741,2743,2765],{"className":2742},[580],[577,2744,2746],{"className":2745},[584],[586,2747,2748],{"xmlns":588},[590,2749,2750,2762],{},[593,2751,2752,2754,2756,2758,2760],{},[596,2753,883],{},[1017,2755,1024],{},[1423,2757,1757],{},[1565,2759,1567],{},[1565,2761,1570],{},[600,2763,2764],{"encoding":602},"b = 6\\,\\text{cm}",[577,2766,2768,2786],{"className":2767,"ariaHidden":607},[606],[577,2769,2771,2774,2777,2780,2783],{"className":2770},[611],[577,2772],{"className":2773,"style":895},[615],[577,2775,883],{"className":2776},[620,621],[577,2778],{"className":2779,"style":1177},[1038],[577,2781,1024],{"className":2782},[1181],[577,2784],{"className":2785,"style":1177},[1038],[577,2787,2789,2792,2795,2798],{"className":2788},[611],[577,2790],{"className":2791,"style":1601},[615],[577,2793,1757],{"className":2794},[620],[577,2796],{"className":2797,"style":1129},[1038],[577,2799,2801],{"className":2800},[620,1611],[577,2802,1570],{"className":2803},[620],[577,2805,2807,2830],{"className":2806},[580],[577,2808,2810],{"className":2809},[584],[586,2811,2812],{"xmlns":588},[590,2813,2814,2827],{},[593,2815,2816,2818,2820],{},[596,2817,698],{},[1017,2819,1024],{},[1420,2821,2822,2825],{},[1423,2823,2824],{},"70",[1017,2826,1428],{},[600,2828,2829],{"encoding":602},"\\alpha = 70^\\circ",[577,2831,2833,2851],{"className":2832,"ariaHidden":607},[606],[577,2834,2836,2839,2842,2845,2848],{"className":2835},[611],[577,2837],{"className":2838,"style":711},[615],[577,2840,698],{"className":2841,"style":715},[620,621],[577,2843],{"className":2844,"style":1177},[1038],[577,2846,1024],{"className":2847},[1181],[577,2849],{"className":2850,"style":1177},[1038],[577,2852,2854,2857,2860],{"className":2853},[611],[577,2855],{"className":2856,"style":1496},[615],[577,2858,2654],{"className":2859},[620],[577,2861,2863,2866],{"className":2862},[620],[577,2864,1507],{"className":2865},[620],[577,2867,2869],{"className":2868},[1511],[577,2870,2872],{"className":2871},[1100],[577,2873,2875],{"className":2874},[1105],[577,2876,2878],{"className":2877,"style":1496},[1109],[577,2879,2880,2883],{"style":1523},[577,2881],{"className":2882,"style":1527},[1117],[577,2884,2886],{"className":2885},[1531,1532,1533,1534],[577,2887,1428],{"className":2888},[1364,1534],". Gesucht ist ",[577,2891,2893,2906],{"className":2892},[580],[577,2894,2896],{"className":2895},[584],[586,2897,2898],{"xmlns":588},[590,2899,2900,2904],{},[593,2901,2902],{},[596,2903,730],{},[600,2905,733],{"encoding":602},[577,2907,2909],{"className":2908,"ariaHidden":607},[606],[577,2910,2912,2915],{"className":2911},[611],[577,2913],{"className":2914,"style":743},[615],[577,2916,730],{"className":2917,"style":747},[620,621],[577,2919,2921],{"className":2920},[992],[577,2922,2924,2986],{"className":2923},[580],[577,2925,2927],{"className":2926},[584],[586,2928,2929],{"xmlns":588,"display":1001},[590,2930,2931,2983],{},[593,2932,2933,2935,2937,2939,2941,2961,2963,2966,2968,2970,2972,2974,2976],{},[596,2934,1015],{},[1017,2936,1019],{},[596,2938,730],{},[1017,2940,1024],{},[1007,2942,2943,2959],{},[593,2944,2945,2947,2949,2951,2953],{},[1423,2946,1757],{},[1017,2948,1058],{},[596,2950,1015],{},[1017,2952,1019],{},[1420,2954,2955,2957],{},[1423,2956,2824],{},[1017,2958,1428],{},[1423,2960,2361],{},[1017,2962,1900],{},[1423,2964,2965],{},"0,7048",[1038,2967],{"width":1040},[1017,2969,1043],{},[1038,2971],{"width":1040},[596,2973,730],{},[1017,2975,1900],{},[1420,2977,2978,2981],{},[1423,2979,2980],{},"44,81",[1017,2982,1428],{},[600,2984,2985],{"encoding":602},"\\sin \\beta = \\frac{6 \\cdot \\sin 70^\\circ}{8} \\approx 0{,}7048\n\\quad\\Rightarrow\\quad\n\\beta \\approx 44{,}81^\\circ",[577,2987,2989,3013,3137,3171,3189],{"className":2988,"ariaHidden":607},[606],[577,2990,2992,2995,2998,3001,3004,3007,3010],{"className":2991},[611],[577,2993],{"className":2994,"style":743},[615],[577,2996,1015],{"className":2997},[1125],[577,2999],{"className":3000,"style":1129},[1038],[577,3002,730],{"className":3003,"style":747},[620,621],[577,3005],{"className":3006,"style":1177},[1038],[577,3008,1024],{"className":3009},[1181],[577,3011],{"className":3012,"style":1177},[1038],[577,3014,3016,3019,3128,3131,3134],{"className":3015},[611],[577,3017],{"className":3018,"style":1938},[615],[577,3020,3022,3025,3125],{"className":3021},[620],[577,3023],{"className":3024},[1092,1093],[577,3026,3028],{"className":3027},[1007],[577,3029,3031,3117],{"className":3030},[1100,1101],[577,3032,3034,3114],{"className":3033},[1105],[577,3035,3037,3048,3056],{"className":3036,"style":1957},[1109],[577,3038,3039,3042],{"style":1113},[577,3040],{"className":3041,"style":1118},[1117],[577,3043,3045],{"className":3044},[620],[577,3046,2361],{"className":3047},[620],[577,3049,3050,3053],{"style":1135},[577,3051],{"className":3052,"style":1118},[1117],[577,3054],{"className":3055,"style":1143},[1142],[577,3057,3058,3061],{"style":1146},[577,3059],{"className":3060,"style":1118},[1117],[577,3062,3064,3067,3070,3073,3076,3079,3082,3085],{"className":3063},[620],[577,3065,1757],{"className":3066},[620],[577,3068],{"className":3069,"style":1360},[1038],[577,3071,1058],{"className":3072},[1364],[577,3074],{"className":3075,"style":1360},[1038],[577,3077,1015],{"className":3078},[1125],[577,3080],{"className":3081,"style":1129},[1038],[577,3083,2654],{"className":3084},[620],[577,3086,3088,3091],{"className":3087},[620],[577,3089,1507],{"className":3090},[620],[577,3092,3094],{"className":3093},[1511],[577,3095,3097],{"className":3096},[1100],[577,3098,3100],{"className":3099},[1105],[577,3101,3103],{"className":3102,"style":1496},[1109],[577,3104,3105,3108],{"style":1523},[577,3106],{"className":3107,"style":1527},[1117],[577,3109,3111],{"className":3110},[1531,1532,1533,1534],[577,3112,1428],{"className":3113},[1364,1534],[577,3115,1160],{"className":3116},[1159],[577,3118,3120],{"className":3119},[1105],[577,3121,3123],{"className":3122,"style":1167},[1109],[577,3124],{},[577,3126],{"className":3127},[1173,1093],[577,3129],{"className":3130,"style":1177},[1038],[577,3132,1900],{"className":3133},[1181],[577,3135],{"className":3136,"style":1177},[1038],[577,3138,3140,3143,3146,3152,3156,3159,3162,3165,3168],{"className":3139},[611],[577,3141],{"className":3142,"style":2110},[615],[577,3144,1507],{"className":3145},[620],[577,3147,3149],{"className":3148},[620],[577,3150,2121],{"className":3151},[2120],[577,3153,3155],{"className":3154},[620],"7048",[577,3157],{"className":3158,"style":1265},[1038],[577,3160],{"className":3161,"style":1177},[1038],[577,3163,1043],{"className":3164},[1181],[577,3166],{"className":3167,"style":1265},[1038],[577,3169],{"className":3170,"style":1177},[1038],[577,3172,3174,3177,3180,3183,3186],{"className":3173},[611],[577,3175],{"className":3176,"style":743},[615],[577,3178,730],{"className":3179,"style":747},[620,621],[577,3181],{"className":3182,"style":1177},[1038],[577,3184,1900],{"className":3185},[1181],[577,3187],{"className":3188,"style":1177},[1038],[577,3190,3192,3196,3200,3206,3209],{"className":3191},[611],[577,3193],{"className":3194,"style":3195},[615],"height:0.9186em;vertical-align:-0.1944em;",[577,3197,3199],{"className":3198},[620],"44",[577,3201,3203],{"className":3202},[620],[577,3204,2121],{"className":3205},[2120],[577,3207,2361],{"className":3208},[620],[577,3210,3212,3216],{"className":3211},[620],[577,3213,3215],{"className":3214},[620],"1",[577,3217,3219],{"className":3218},[1511],[577,3220,3222],{"className":3221},[1100],[577,3223,3225],{"className":3224},[1105],[577,3226,3229],{"className":3227,"style":3228},[1109],"height:0.7241em;",[577,3230,3232,3235],{"style":3231},"top:-3.113em;margin-right:0.05em;",[577,3233],{"className":3234,"style":1527},[1117],[577,3236,3238],{"className":3237},[1531,1532,1533,1534],[577,3239,1428],{"className":3240},[1364,1534],[564,3242,3243,3244,3272,3273,3301,3302,3330,3331,3359,3360,3470,3471,3499,3500,985],{},"Da ",[577,3245,3247,3260],{"className":3246},[580],[577,3248,3250],{"className":3249},[584],[586,3251,3252],{"xmlns":588},[590,3253,3254,3258],{},[593,3255,3256],{},[596,3257,883],{},[600,3259,883],{"encoding":602},[577,3261,3263],{"className":3262,"ariaHidden":607},[606],[577,3264,3266,3269],{"className":3265},[611],[577,3267],{"className":3268,"style":895},[615],[577,3270,883],{"className":3271},[620,621]," kürzer ist als ",[577,3274,3276,3289],{"className":3275},[580],[577,3277,3279],{"className":3278},[584],[586,3280,3281],{"xmlns":588},[590,3282,3283,3287],{},[593,3284,3285],{},[596,3286,795],{},[600,3288,795],{"encoding":602},[577,3290,3292],{"className":3291,"ariaHidden":607},[606],[577,3293,3295,3298],{"className":3294},[611],[577,3296],{"className":3297,"style":711},[615],[577,3299,795],{"className":3300},[620,621],", muss ",[577,3303,3305,3318],{"className":3304},[580],[577,3306,3308],{"className":3307},[584],[586,3309,3310],{"xmlns":588},[590,3311,3312,3316],{},[593,3313,3314],{},[596,3315,730],{},[600,3317,733],{"encoding":602},[577,3319,3321],{"className":3320,"ariaHidden":607},[606],[577,3322,3324,3327],{"className":3323},[611],[577,3325],{"className":3326,"style":743},[615],[577,3328,730],{"className":3329,"style":747},[620,621]," kleiner sein als ",[577,3332,3334,3347],{"className":3333},[580],[577,3335,3337],{"className":3336},[584],[586,3338,3339],{"xmlns":588},[590,3340,3341,3345],{},[593,3342,3343],{},[596,3344,698],{},[600,3346,701],{"encoding":602},[577,3348,3350],{"className":3349,"ariaHidden":607},[606],[577,3351,3353,3356],{"className":3352},[611],[577,3354],{"className":3355,"style":711},[615],[577,3357,698],{"className":3358,"style":715},[620,621],". Da ",[577,3361,3363,3391],{"className":3362},[580],[577,3364,3366],{"className":3365},[584],[586,3367,3368],{"xmlns":588},[590,3369,3370,3388],{},[593,3371,3372,3374,3377,3379,3381],{},[596,3373,730],{},[1017,3375,3376],{},"\u003C",[596,3378,698],{},[1017,3380,3376],{},[1420,3382,3383,3386],{},[1423,3384,3385],{},"90",[1017,3387,1428],{},[600,3389,3390],{"encoding":602},"\\beta \u003C \\alpha \u003C 90^\\circ",[577,3392,3394,3412,3431],{"className":3393,"ariaHidden":607},[606],[577,3395,3397,3400,3403,3406,3409],{"className":3396},[611],[577,3398],{"className":3399,"style":743},[615],[577,3401,730],{"className":3402,"style":747},[620,621],[577,3404],{"className":3405,"style":1177},[1038],[577,3407,3376],{"className":3408},[1181],[577,3410],{"className":3411,"style":1177},[1038],[577,3413,3415,3419,3422,3425,3428],{"className":3414},[611],[577,3416],{"className":3417,"style":3418},[615],"height:0.5782em;vertical-align:-0.0391em;",[577,3420,698],{"className":3421,"style":715},[620,621],[577,3423],{"className":3424,"style":1177},[1038],[577,3426,3376],{"className":3427},[1181],[577,3429],{"className":3430,"style":1177},[1038],[577,3432,3434,3437,3441],{"className":3433},[611],[577,3435],{"className":3436,"style":1496},[615],[577,3438,3440],{"className":3439},[620],"9",[577,3442,3444,3447],{"className":3443},[620],[577,3445,1507],{"className":3446},[620],[577,3448,3450],{"className":3449},[1511],[577,3451,3453],{"className":3452},[1100],[577,3454,3456],{"className":3455},[1105],[577,3457,3459],{"className":3458,"style":1496},[1109],[577,3460,3461,3464],{"style":1523},[577,3462],{"className":3463,"style":1527},[1117],[577,3465,3467],{"className":3466},[1531,1532,1533,1534],[577,3468,1428],{"className":3469},[1364,1534],", ist ",[577,3472,3474,3487],{"className":3473},[580],[577,3475,3477],{"className":3476},[584],[586,3478,3479],{"xmlns":588},[590,3480,3481,3485],{},[593,3482,3483],{},[596,3484,730],{},[600,3486,733],{"encoding":602},[577,3488,3490],{"className":3489,"ariaHidden":607},[606],[577,3491,3493,3496],{"className":3492},[611],[577,3494],{"className":3495,"style":743},[615],[577,3497,730],{"className":3498,"style":747},[620,621]," spitz und die Lösung eindeutig. Es folgt ",[577,3501,3503,3550],{"className":3502},[580],[577,3504,3506],{"className":3505},[584],[586,3507,3508],{"xmlns":588},[590,3509,3510,3547],{},[593,3511,3512,3514,3516,3522,3524,3530,3532,3538,3540],{},[596,3513,762],{},[1017,3515,1900],{},[1420,3517,3518,3520],{},[1423,3519,1425],{},[1017,3521,1428],{},[1017,3523,2162],{},[1420,3525,3526,3528],{},[1423,3527,2824],{},[1017,3529,1428],{},[1017,3531,2162],{},[1420,3533,3534,3536],{},[1423,3535,2980],{},[1017,3537,1428],{},[1017,3539,1024],{},[1420,3541,3542,3545],{},[1423,3543,3544],{},"65,19",[1017,3546,1428],{},[600,3548,3549],{"encoding":602},"\\gamma \\approx 180^\\circ - 70^\\circ - 44{,}81^\\circ = 65{,}19^\\circ",[577,3551,3553,3572,3619,3666,3723],{"className":3552,"ariaHidden":607},[606],[577,3554,3556,3560,3563,3566,3569],{"className":3555},[611],[577,3557],{"className":3558,"style":3559},[615],"height:0.6776em;vertical-align:-0.1944em;",[577,3561,762],{"className":3562,"style":779},[620,621],[577,3564],{"className":3565,"style":1177},[1038],[577,3567,1900],{"className":3568},[1181],[577,3570],{"className":3571,"style":1177},[1038],[577,3573,3575,3578,3581,3610,3613,3616],{"className":3574},[611],[577,3576],{"className":3577,"style":2216},[615],[577,3579,1500],{"className":3580},[620],[577,3582,3584,3587],{"className":3583},[620],[577,3585,1507],{"className":3586},[620],[577,3588,3590],{"className":3589},[1511],[577,3591,3593],{"className":3592},[1100],[577,3594,3596],{"className":3595},[1105],[577,3597,3599],{"className":3598,"style":1496},[1109],[577,3600,3601,3604],{"style":1523},[577,3602],{"className":3603,"style":1527},[1117],[577,3605,3607],{"className":3606},[1531,1532,1533,1534],[577,3608,1428],{"className":3609},[1364,1534],[577,3611],{"className":3612,"style":1360},[1038],[577,3614,2162],{"className":3615},[1364],[577,3617],{"className":3618,"style":1360},[1038],[577,3620,3622,3625,3628,3657,3660,3663],{"className":3621},[611],[577,3623],{"className":3624,"style":2216},[615],[577,3626,2654],{"className":3627},[620],[577,3629,3631,3634],{"className":3630},[620],[577,3632,1507],{"className":3633},[620],[577,3635,3637],{"className":3636},[1511],[577,3638,3640],{"className":3639},[1100],[577,3641,3643],{"className":3642},[1105],[577,3644,3646],{"className":3645,"style":1496},[1109],[577,3647,3648,3651],{"style":1523},[577,3649],{"className":3650,"style":1527},[1117],[577,3652,3654],{"className":3653},[1531,1532,1533,1534],[577,3655,1428],{"className":3656},[1364,1534],[577,3658],{"className":3659,"style":1360},[1038],[577,3661,2162],{"className":3662},[1364],[577,3664],{"className":3665,"style":1360},[1038],[577,3667,3669,3673,3676,3682,3685,3714,3717,3720],{"className":3668},[611],[577,3670],{"className":3671,"style":3672},[615],"height:0.8686em;vertical-align:-0.1944em;",[577,3674,3199],{"className":3675},[620],[577,3677,3679],{"className":3678},[620],[577,3680,2121],{"className":3681},[2120],[577,3683,2361],{"className":3684},[620],[577,3686,3688,3691],{"className":3687},[620],[577,3689,3215],{"className":3690},[620],[577,3692,3694],{"className":3693},[1511],[577,3695,3697],{"className":3696},[1100],[577,3698,3700],{"className":3699},[1105],[577,3701,3703],{"className":3702,"style":1496},[1109],[577,3704,3705,3708],{"style":1523},[577,3706],{"className":3707,"style":1527},[1117],[577,3709,3711],{"className":3710},[1531,1532,1533,1534],[577,3712,1428],{"className":3713},[1364,1534],[577,3715],{"className":3716,"style":1177},[1038],[577,3718,1024],{"className":3719},[1181],[577,3721],{"className":3722,"style":1177},[1038],[577,3724,3726,3729,3733,3739,3742],{"className":3725},[611],[577,3727],{"className":3728,"style":3672},[615],[577,3730,3732],{"className":3731},[620],"65",[577,3734,3736],{"className":3735},[620],[577,3737,2121],{"className":3738},[2120],[577,3740,3215],{"className":3741},[620],[577,3743,3745,3748],{"className":3744},[620],[577,3746,3440],{"className":3747},[620],[577,3749,3751],{"className":3750},[1511],[577,3752,3754],{"className":3753},[1100],[577,3755,3757],{"className":3756},[1105],[577,3758,3760],{"className":3759,"style":1496},[1109],[577,3761,3762,3765],{"style":1523},[577,3763],{"className":3764,"style":1527},[1117],[577,3766,3768],{"className":3767},[1531,1532,1533,1534],[577,3769,1428],{"className":3770},[1364,1534],[559,3772,3774],{"id":3773},"typische-fehler","Typische Fehler",[3776,3777,3778,3873,4125],"ul",{},[3779,3780,3781,3782,3810,3811,3814,3815,3843,3844,3872],"li",{},"Seite und Winkel falsch zuordnen: Zu ",[577,3783,3785,3798],{"className":3784},[580],[577,3786,3788],{"className":3787},[584],[586,3789,3790],{"xmlns":588},[590,3791,3792,3796],{},[593,3793,3794],{},[596,3795,795],{},[600,3797,795],{"encoding":602},[577,3799,3801],{"className":3800,"ariaHidden":607},[606],[577,3802,3804,3807],{"className":3803},[611],[577,3805],{"className":3806,"style":711},[615],[577,3808,795],{"className":3809},[620,621]," gehört der Winkel ",[568,3812,3813],{},"gegenüber"," von ",[577,3816,3818,3831],{"className":3817},[580],[577,3819,3821],{"className":3820},[584],[586,3822,3823],{"xmlns":588},[590,3824,3825,3829],{},[593,3826,3827],{},[596,3828,795],{},[600,3830,795],{"encoding":602},[577,3832,3834],{"className":3833,"ariaHidden":607},[606],[577,3835,3837,3840],{"className":3836},[611],[577,3838],{"className":3839,"style":711},[615],[577,3841,795],{"className":3842},[620,621],", nicht ein Winkel, der an ",[577,3845,3847,3860],{"className":3846},[580],[577,3848,3850],{"className":3849},[584],[586,3851,3852],{"xmlns":588},[590,3853,3854,3858],{},[593,3855,3856],{},[596,3857,795],{},[600,3859,795],{"encoding":602},[577,3861,3863],{"className":3862,"ariaHidden":607},[606],[577,3864,3866,3869],{"className":3865},[611],[577,3867],{"className":3868,"style":711},[615],[577,3870,795],{"className":3871},[620,621]," anliegt.",[3779,3874,3875,3876,3947,3948,4034,4035,4034,4038,4124],{},"Den zweiten möglichen Winkel übersehen. Aus ",[577,3877,3879,3902],{"className":3878},[580],[577,3880,3882],{"className":3881},[584],[586,3883,3884],{"xmlns":588},[590,3885,3886,3899],{},[593,3887,3888,3890,3892,3894,3896],{},[596,3889,1015],{},[1017,3891,1019],{},[596,3893,730],{},[1017,3895,1024],{},[1423,3897,3898],{},"0,5",[600,3900,3901],{"encoding":602},"\\sin \\beta = 0{,}5",[577,3903,3905,3929],{"className":3904,"ariaHidden":607},[606],[577,3906,3908,3911,3914,3917,3920,3923,3926],{"className":3907},[611],[577,3909],{"className":3910,"style":743},[615],[577,3912,1015],{"className":3913},[1125],[577,3915],{"className":3916,"style":1129},[1038],[577,3918,730],{"className":3919,"style":747},[620,621],[577,3921],{"className":3922,"style":1177},[1038],[577,3924,1024],{"className":3925},[1181],[577,3927],{"className":3928,"style":1177},[1038],[577,3930,3932,3935,3938,3944],{"className":3931},[611],[577,3933],{"className":3934,"style":2110},[615],[577,3936,1507],{"className":3937},[620],[577,3939,3941],{"className":3940},[620],[577,3942,2121],{"className":3943},[2120],[577,3945,1563],{"className":3946},[620]," folgt ",[577,3949,3951,3974],{"className":3950},[580],[577,3952,3954],{"className":3953},[584],[586,3955,3956],{"xmlns":588},[590,3957,3958,3971],{},[593,3959,3960,3962,3964],{},[596,3961,730],{},[1017,3963,1024],{},[1420,3965,3966,3969],{},[1423,3967,3968],{},"30",[1017,3970,1428],{},[600,3972,3973],{"encoding":602},"\\beta = 30^\\circ",[577,3975,3977,3995],{"className":3976,"ariaHidden":607},[606],[577,3978,3980,3983,3986,3989,3992],{"className":3979},[611],[577,3981],{"className":3982,"style":743},[615],[577,3984,730],{"className":3985,"style":747},[620,621],[577,3987],{"className":3988,"style":1177},[1038],[577,3990,1024],{"className":3991},[1181],[577,3993],{"className":3994,"style":1177},[1038],[577,3996,3998,4001,4005],{"className":3997},[611],[577,3999],{"className":4000,"style":1496},[615],[577,4002,4004],{"className":4003},[620],"3",[577,4006,4008,4011],{"className":4007},[620],[577,4009,1507],{"className":4010},[620],[577,4012,4014],{"className":4013},[1511],[577,4015,4017],{"className":4016},[1100],[577,4018,4020],{"className":4019},[1105],[577,4021,4023],{"className":4022,"style":1496},[1109],[577,4024,4025,4028],{"style":1523},[577,4026],{"className":4027,"style":1527},[1117],[577,4029,4031],{"className":4030},[1531,1532,1533,1534],[577,4032,1428],{"className":4033},[1364,1534]," ",[568,4036,4037],{},"oder",[577,4039,4041,4064],{"className":4040},[580],[577,4042,4044],{"className":4043},[584],[586,4045,4046],{"xmlns":588},[590,4047,4048,4061],{},[593,4049,4050,4052,4054],{},[596,4051,730],{},[1017,4053,1024],{},[1420,4055,4056,4059],{},[1423,4057,4058],{},"150",[1017,4060,1428],{},[600,4062,4063],{"encoding":602},"\\beta = 150^\\circ",[577,4065,4067,4085],{"className":4066,"ariaHidden":607},[606],[577,4068,4070,4073,4076,4079,4082],{"className":4069},[611],[577,4071],{"className":4072,"style":743},[615],[577,4074,730],{"className":4075,"style":747},[620,621],[577,4077],{"className":4078,"style":1177},[1038],[577,4080,1024],{"className":4081},[1181],[577,4083],{"className":4084,"style":1177},[1038],[577,4086,4088,4091,4095],{"className":4087},[611],[577,4089],{"className":4090,"style":1496},[615],[577,4092,4094],{"className":4093},[620],"15",[577,4096,4098,4101],{"className":4097},[620],[577,4099,1507],{"className":4100},[620],[577,4102,4104],{"className":4103},[1511],[577,4105,4107],{"className":4106},[1100],[577,4108,4110],{"className":4109},[1105],[577,4111,4113],{"className":4112,"style":1496},[1109],[577,4114,4115,4118],{"style":1523},[577,4116],{"className":4117,"style":1527},[1117],[577,4119,4121],{"className":4120},[1531,1532,1533,1534],[577,4122,1428],{"className":4123},[1364,1534],". Liegt der gegebene Winkel der kürzeren der beiden gegebenen Seiten gegenüber, kann es zwei Dreiecke geben; dann beide Fälle prüfen.",[3779,4126,4127],{},"Den Sinussatz verwenden, obwohl kein Paar aus Seite und gegenüberliegendem Winkel bekannt ist (z.B. drei Seiten gegeben). Dann braucht man den Kosinussatz.",{"title":4129,"searchDepth":4130,"depth":4130,"links":4131},"",2,[4132,4133,4134],{"id":561,"depth":4130,"text":562},{"id":1540,"depth":4130,"text":1541},{"id":3773,"depth":4130,"text":3774},[4136,4139,4141,4144,4146,4149,4152,4155,4158,4161],{"lhs":4137,"rhs":4138},"sqrt((w - u)^2 + v^2) \u002F sin(atan2(v, u))","sqrt(u^2 + v^2) \u002F sin(atan2(v, w - u))",{"lhs":4137,"rhs":4140},"w \u002F sin(pi - atan2(v, u) - atan2(v, w - u))",{"lhs":4142,"rhs":4143},"round(5 * sin(60*pi\u002F180) \u002F sin(40*pi\u002F180), 2)","6.74",{"lhs":4145,"rhs":2183},"180 - 40 - 60",{"lhs":4147,"rhs":4148},"round(5 * sin(80*pi\u002F180) \u002F sin(40*pi\u002F180), 2)","7.66",{"lhs":4150,"rhs":4151},"round(6 * sin(70*pi\u002F180) \u002F 8, 4)","0.7048",{"lhs":4153,"rhs":4154},"round(asin(6 * sin(70*pi\u002F180) \u002F 8) * 180\u002Fpi, 2)","44.81",{"lhs":4156,"rhs":4157},"180 - 70 - 44.81","65.19",{"lhs":4159,"rhs":4160},"sin(30*pi\u002F180)","0.5",{"lhs":4162,"rhs":4160},"sin(150*pi\u002F180)","\\text{beliebiges Dreieck mit}\\ \\alpha + \\beta + \\gamma = 180^\\circ","\u003Cspan class=\"katex\">beliebiges Dreieck mit\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>β\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha + \\beta + \\gamma = 180^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0528em;\">β\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6741em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">18\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4168,"x":4169,"y":4172,"unit":4175,"items":4176},"Dreieck ABC, jede Seite liegt dem gleichnamigen Winkel gegenüber (a gegenüber α, b gegenüber β, c gegenüber γ)",[4170,4171],-0.8,8.5,[4173,4174],-0.9,5,32,[4177,4188,4193,4197,4201,4206,4210,4214,4220,4224],{"type":4178,"points":4179,"fill":4187},"polygon",[4180,4182,4184],[4181,4181],0,[4183,4181],7.66,[4185,4186],5.163,4.333,true,{"type":4189,"at":4190,"from":4191,"to":4192,"label":698},"angle",[4181,4181],[4183,4181],[4185,4186],{"type":4189,"at":4194,"from":4195,"to":4196,"label":730},[4183,4181],[4185,4186],[4181,4181],{"type":4189,"at":4198,"from":4199,"to":4200,"label":762},[4185,4186],[4181,4181],[4183,4181],{"type":4202,"at":4203,"text":795},"label",[4204,4205],6.8,2.39,{"type":4202,"at":4207,"text":883},[4208,4209],2.29,2.51,{"type":4202,"at":4211,"text":942},[4212,4213],3.83,-0.45,{"type":4215,"at":4216,"label":598,"offset":4217},"point",[4181,4181],[4218,4219],-18,10,{"type":4215,"at":4221,"label":637,"offset":4222},[4183,4181],[4223,4219],6,{"type":4215,"at":4225,"label":667,"offset":4226},[4185,4186],[4223,4227],-10,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 297.6 188.8\" width=\"297.6\" height=\"188.8\" role=\"img\" aria-label=\"Dreieck ABC, jede Seite liegt dem gleichnamigen Winkel gegenüber (a gegenüber α, b gegenüber β, c gegenüber γ)\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-law-of-sines-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-law-of-sines-clip\">\u003Crect x=\"0\" y=\"0\" width=\"297.6\" height=\"188.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"25.6,160 270.72,160 190.82,21.34\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 25.6 160 L 47.6 160 A 22 22 0 0 0 42.45 145.86 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"57.55\" y=\"148.37\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Cpath d=\"M 270.72 160 L 259.74 140.94 A 22 22 0 0 0 248.72 160 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"241.28\" y=\"142.99\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">β\u003C\u002Ftext>\u003Cpath d=\"M 190.82 21.34 L 173.97 35.48 A 22 22 0 0 0 201.8 40.4 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"184.9\" y=\"54.82\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">γ\u003C\u002Ftext>\u003Ctext x=\"243.2\" y=\"83.52\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"98.88\" y=\"79.68\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"148.16\" y=\"174.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ccircle cx=\"25.6\" cy=\"160\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"7.600000000000001\" y=\"170\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"270.72\" cy=\"160\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"276.72\" y=\"170\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"190.82\" cy=\"21.34\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"196.82\" y=\"11.34\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","law-of-sines","\\frac{a}{\\sin \\alpha} = \\frac{b}{\\sin \\beta} = \\frac{c}{\\sin \\gamma}","\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>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>b\u003C\u002Fmi>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>β\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>c\u003C\u002Fmi>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{a}{\\sin \\alpha} = \\frac{b}{\\sin \\beta} = \\frac{c}{\\sin \\gamma}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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>\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 mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0528em;\">β\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 mathnormal\">b\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>\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:1.988em;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:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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