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1479,"style":1023},[767],[574,1481,1483,1486,1489,1492,1495,1498,1501],{"className":1482},[608],[574,1484],{"className":1485,"style":892},[612],[574,1487,915],{"className":1488},[617],[574,1490,595],{"className":1491},[617,618],[574,1493,702],{"className":1494},[617,618],[574,1496],{"className":1497,"style":1023},[767],[574,1499,1119],{"className":1500},[828],[574,1502],{"className":1503,"style":1023},[767],[574,1505,1507,1511,1514,1517],{"className":1506},[608],[574,1508],{"className":1509,"style":1510},[612],"height:0.8889em;vertical-align:-0.1944em;",[574,1512,844],{"className":1513},[869],[574,1515],{"className":1516,"style":873},[767],[574,1518,1168],{"className":1519,"style":1520},[617,618],"margin-right:0.0528em;",[565,1522,1523],{},"Sind alle drei Seiten bekannt, stellt man nach dem Kosinus um und erhält einen Winkel:",[574,1525,1527],{"className":1526},[1072],[574,1528,1530,1585],{"className":1529},[577],[574,1531,1533],{"className":1532},[581],[583,1534,1535],{"xmlns":585,"display":1081},[587,1536,1537,1582],{},[590,1538,1539,1541,1543,1545,1547],{},[593,1540,844],{},[736,1542,847],{},[593,1544,665],{},[736,1546,738],{},[1548,1549,1550,1574],"mfrac",{},[590,1551,1552,1558,1560,1566,1568],{},[740,1553,1554,1556],{},[593,1555,595],{},[743,1557,915],{},[736,1559,926],{},[740,1561,1562,1564],{},[593,1563,634],{},[743,1565,915],{},[736,1567,1110],{},[740,1569,1570,1572],{},[593,1571,702],{},[743,1573,915],{},[590,1575,1576,1578,1580],{},[743,1577,915],{},[593,1579,595],{},[593,1581,634],{},[597,1583,1584],{"encoding":599},"\\cos \\gamma = \\frac{a^2 + b^2 - c^2}{2ab}",[574,1586,1588,1612],{"className":1587,"ariaHidden":604},[603],[574,1589,1591,1594,1597,1600,1603,1606,1609],{"className":1590},[608],[574,1592],{"className":1593,"style":678},[612],[574,1595,844],{"className":1596},[869],[574,1598],{"className":1599,"style":873},[767],[574,1601,665],{"className":1602,"style":682},[617,618],[574,1604],{"className":1605,"style":768},[767],[574,1607,738],{"className":1608},[772],[574,1610],{"className":1611,"style":768},[767],[574,1613,1615,1619],{"className":1614},[608],[574,1616],{"className":1617,"style":1618},[612],"height:2.1771em;vertical-align:-0.686em;",[574,1620,1622,1627,1797],{"className":1621},[617],[574,1623],{"className":1624},[1625,1626],"mopen","nulldelimiter",[574,1628,1630],{"className":1629},[1548],[574,1631,1634,1788],{"className":1632},[801,1633],"vlist-t2",[574,1635,1637,1783],{"className":1636},[805],[574,1638,1641,1658,1669],{"className":1639,"style":1640},[809],"height:1.4911em;",[574,1642,1644,1648],{"style":1643},"top:-2.314em;",[574,1645],{"className":1646,"style":1647},[816],"height:3em;",[574,1649,1651,1654],{"className":1650},[617],[574,1652,915],{"className":1653},[617],[574,1655,1657],{"className":1656},[617,618],"ab",[574,1659,1661,1664],{"style":1660},"top:-3.23em;",[574,1662],{"className":1663,"style":1647},[816],[574,1665],{"className":1666,"style":1668},[1667],"frac-line","border-bottom-width:0.04em;",[574,1670,1672,1675],{"style":1671},"top:-3.677em;",[574,1673],{"className":1674,"style":1647},[816],[574,1676,1678,1707,1710,1713,1716,1745,1748,1751,1754],{"className":1677},[617],[574,1679,1681,1684],{"className":1680},[617],[574,1682,595],{"className":1683},[617,618],[574,1685,1687],{"className":1686},[797],[574,1688,1690],{"className":1689},[801],[574,1691,1693],{"className":1692},[805],[574,1694,1696],{"className":1695,"style":945},[809],[574,1697,1698,1701],{"style":812},[574,1699],{"className":1700,"style":817},[816],[574,1702,1704],{"className":1703},[821,822,823,824],[574,1705,915],{"className":1706},[617,824],[574,1708],{"className":1709,"style":1023},[767],[574,1711,926],{"className":1712},[828],[574,1714],{"className":1715,"style":1023},[767],[574,1717,1719,1722],{"className":1718},[617],[574,1720,634],{"className":1721},[617,618],[574,1723,1725],{"className":1724},[797],[574,1726,1728],{"className":1727},[801],[574,1729,1731],{"className":1730},[805],[574,1732,1734],{"className":1733,"style":945},[809],[574,1735,1736,1739],{"style":812},[574,1737],{"className":1738,"style":817},[816],[574,1740,1742],{"className":1741},[821,822,823,824],[574,1743,915],{"className":1744},[617,824],[574,1746],{"className":1747,"style":1023},[767],[574,1749,1110],{"className":1750},[828],[574,1752],{"className":1753,"style":1023},[767],[574,1755,1757,1760],{"className":1756},[617],[574,1758,702],{"className":1759},[617,618],[574,1761,1763],{"className":1762},[797],[574,1764,1766],{"className":1765},[801],[574,1767,1769],{"className":1768},[805],[574,1770,1772],{"className":1771,"style":945},[809],[574,1773,1774,1777],{"style":812},[574,1775],{"className":1776,"style":817},[816],[574,1778,1780],{"className":1779},[821,822,823,824],[574,1781,915],{"className":1782},[617,824],[574,1784,1787],{"className":1785},[1786],"vlist-s","​",[574,1789,1791],{"className":1790},[805],[574,1792,1795],{"className":1793,"style":1794},[809],"height:0.686em;",[574,1796],{},[574,1798],{"className":1799},[1800,1626],"mclose",[560,1802,1804],{"id":1803},"beispiele","Beispiele",[565,1806,1807,1808,1877,1878,1943,1944,2030],{},"Gegeben sind ",[574,1809,1811,1837],{"className":1810},[577],[574,1812,1814],{"className":1813},[581],[583,1815,1816],{"xmlns":585},[587,1817,1818,1834],{},[590,1819,1820,1822,1824,1827,1831],{},[593,1821,595],{},[736,1823,738],{},[743,1825,1826],{},"5",[1828,1829,1830],"mtext",{}," ",[1828,1832,1833],{},"cm",[597,1835,1836],{"encoding":599},"a = 5\\,\\text{cm}",[574,1838,1840,1858],{"className":1839,"ariaHidden":604},[603],[574,1841,1843,1846,1849,1852,1855],{"className":1842},[608],[574,1844],{"className":1845,"style":613},[612],[574,1847,595],{"className":1848},[617,618],[574,1850],{"className":1851,"style":768},[767],[574,1853,738],{"className":1854},[772],[574,1856],{"className":1857,"style":768},[767],[574,1859,1861,1864,1867,1870],{"className":1860},[608],[574,1862],{"className":1863,"style":892},[612],[574,1865,1826],{"className":1866},[617],[574,1868],{"className":1869,"style":873},[767],[574,1871,1874],{"className":1872},[617,1873],"text",[574,1875,1833],{"className":1876},[617],", ",[574,1879,1881,1904],{"className":1880},[577],[574,1882,1884],{"className":1883},[581],[583,1885,1886],{"xmlns":585},[587,1887,1888,1901],{},[590,1889,1890,1892,1894,1897,1899],{},[593,1891,634],{},[736,1893,738],{},[743,1895,1896],{},"7",[1828,1898,1830],{},[1828,1900,1833],{},[597,1902,1903],{"encoding":599},"b = 7\\,\\text{cm}",[574,1905,1907,1925],{"className":1906,"ariaHidden":604},[603],[574,1908,1910,1913,1916,1919,1922],{"className":1909},[608],[574,1911],{"className":1912,"style":646},[612],[574,1914,634],{"className":1915},[617,618],[574,1917],{"className":1918,"style":768},[767],[574,1920,738],{"className":1921},[772],[574,1923],{"className":1924,"style":768},[767],[574,1926,1928,1931,1934,1937],{"className":1927},[608],[574,1929],{"className":1930,"style":892},[612],[574,1932,1896],{"className":1933},[617],[574,1935],{"className":1936,"style":873},[767],[574,1938,1940],{"className":1939},[617,1873],[574,1941,1833],{"className":1942},[617]," und der eingeschlossene Winkel ",[574,1945,1947,1970],{"className":1946},[577],[574,1948,1950],{"className":1949},[581],[583,1951,1952],{"xmlns":585},[587,1953,1954,1967],{},[590,1955,1956,1958,1960],{},[593,1957,665],{},[736,1959,738],{},[740,1961,1962,1965],{},[743,1963,1964],{},"60",[736,1966,748],{},[597,1968,1969],{"encoding":599},"\\gamma = 60^\\circ",[574,1971,1973,1991],{"className":1972,"ariaHidden":604},[603],[574,1974,1976,1979,1982,1985,1988],{"className":1975},[608],[574,1977],{"className":1978,"style":678},[612],[574,1980,665],{"className":1981,"style":682},[617,618],[574,1983],{"className":1984,"style":768},[767],[574,1986,738],{"className":1987},[772],[574,1989],{"className":1990,"style":768},[767],[574,1992,1994,1997,2001],{"className":1993},[608],[574,1995],{"className":1996,"style":782},[612],[574,1998,2000],{"className":1999},[617],"6",[574,2002,2004,2007],{"className":2003},[617],[574,2005,793],{"className":2006},[617],[574,2008,2010],{"className":2009},[797],[574,2011,2013],{"className":2012},[801],[574,2014,2016],{"className":2015},[805],[574,2017,2019],{"className":2018,"style":782},[809],[574,2020,2021,2024],{"style":812},[574,2022],{"className":2023,"style":817},[816],[574,2025,2027],{"className":2026},[821,822,823,824],[574,2028,748],{"className":2029},[828,824],":",[574,2032,2034],{"className":2033},[1072],[574,2035,2037,2115],{"className":2036},[577],[574,2038,2040],{"className":2039},[581],[583,2041,2042],{"xmlns":585,"display":1081},[587,2043,2044,2112],{},[590,2045,2046,2052,2054,2060,2062,2068,2070,2072,2074,2076,2078,2080,2082,2084,2086,2092,2094,2097,2099,2102,2104,2107,2109],{},[740,2047,2048,2050],{},[593,2049,702],{},[743,2051,915],{},[736,2053,738],{},[740,2055,2056,2058],{},[743,2057,1826],{},[743,2059,915],{},[736,2061,926],{},[740,2063,2064,2066],{},[743,2065,1896],{},[743,2067,915],{},[736,2069,1110],{},[743,2071,915],{},[736,2073,1119],{},[743,2075,1826],{},[736,2077,1119],{},[743,2079,1896],{},[736,2081,1119],{},[593,2083,844],{},[736,2085,847],{},[740,2087,2088,2090],{},[743,2089,1964],{},[736,2091,748],{},[736,2093,738],{},[743,2095,2096],{},"25",[736,2098,926],{},[743,2100,2101],{},"49",[736,2103,1110],{},[743,2105,2106],{},"35",[736,2108,738],{},[743,2110,2111],{},"39",[597,2113,2114],{"encoding":599},"c^2 = 5^2 + 7^2 - 2 \\cdot 5 \\cdot 7 \\cdot \\cos 60^\\circ = 25 + 49 - 35 = 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Der abgezogene Term wird negativ, ",[574,2931,2933,2951],{"className":2932},[577],[574,2934,2936],{"className":2935},[581],[583,2937,2938],{"xmlns":585},[587,2939,2940,2948],{},[590,2941,2942],{},[740,2943,2944,2946],{},[593,2945,702],{},[743,2947,915],{},[597,2949,2950],{"encoding":599},"c^2",[574,2952,2954],{"className":2953,"ariaHidden":604},[603],[574,2955,2957,2960],{"className":2956},[608],[574,2958],{"className":2959,"style":945},[612],[574,2961,2963,2966],{"className":2962},[617],[574,2964,702],{"className":2965},[617,618],[574,2967,2969],{"className":2968},[797],[574,2970,2972],{"className":2971},[801],[574,2973,2975],{"className":2974},[805],[574,2976,2978],{"className":2977,"style":945},[809],[574,2979,2980,2983],{"style":812},[574,2981],{"className":2982,"style":817},[816],[574,2984,2986],{"className":2985},[821,822,823,824],[574,2987,915],{"className":2988},[617,824]," also größer:",[574,2991,2993],{"className":2992},[1072],[574,2994,2996,3071],{"className":2995},[577],[574,2997,2999],{"className":2998},[581],[583,3000,3001],{"xmlns":585,"display":1081},[587,3002,3003,3068],{},[590,3004,3005,3011,3013,3019,3021,3027,3029,3031,3033,3035,3037,3039,3041,3043,3045,3051,3053,3055,3057,3059,3061,3063,3065],{},[740,3006,3007,3009],{},[593,3008,702],{},[743,3010,915],{},[736,3012,738],{},[740,3014,3015,3017],{},[743,3016,1826],{},[743,3018,915],{},[736,3020,926],{},[740,3022,3023,3025],{},[743,3024,1896],{},[743,3026,915],{},[736,3028,1110],{},[743,3030,915],{},[736,3032,1119],{},[743,3034,1826],{},[736,3036,1119],{},[743,3038,1896],{},[736,3040,1119],{},[593,3042,844],{},[736,3044,847],{},[740,3046,3047,3049],{},[743,3048,2753],{},[736,3050,748],{},[736,3052,738],{},[743,3054,2096],{},[736,3056,926],{},[743,3058,2101],{},[736,3060,926],{},[743,3062,2106],{},[736,3064,738],{},[743,3066,3067],{},"109",[597,3069,3070],{"encoding":599},"c^2 = 5^2 + 7^2 - 2 \\cdot 5 \\cdot 7 \\cdot \\cos 120^\\circ = 25 + 49 + 35 = 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= \\sqrt{109}\\,\\text{cm} \\approx 10{,}44\\,\\text{cm}",[574,3416,3418,3436,3507],{"className":3417,"ariaHidden":604},[603],[574,3419,3421,3424,3427,3430,3433],{"className":3420},[608],[574,3422],{"className":3423,"style":613},[612],[574,3425,702],{"className":3426},[617,618],[574,3428],{"className":3429,"style":768},[767],[574,3431,738],{"className":3432},[772],[574,3434],{"className":3435,"style":768},[767],[574,3437,3439,3442,3489,3492,3498,3501,3504],{"className":3438},[608],[574,3440],{"className":3441,"style":2490},[612],[574,3443,3445],{"className":3444},[617,2494],[574,3446,3448,3481],{"className":3447},[801,1633],[574,3449,3451,3478],{"className":3450},[805],[574,3452,3454,3466],{"className":3453,"style":2504},[809],[574,3455,3457,3460],{"className":3456,"style":2509},[2508],[574,3458],{"className":3459,"style":1647},[816],[574,3461,3463],{"className":3462,"style":2516},[617],[574,3464,3067],{"className":3465},[617],[574,3467,3468,3471],{"style":2522},[574,3469],{"className":3470,"style":1647},[816],[574,3472,3474],{"className":3473,"style":2530},[2529],[2532,3475,3476],{"xmlns":2534,"width":2535,"height":2536,"viewBox":2537,"preserveAspectRatio":2538},[2540,3477],{"d":2542},[574,3479,1787],{"className":3480},[1786],[574,3482,3484],{"className":3483},[805],[574,3485,3487],{"className":3486,"style":2552},[809],[574,3488],{},[574,3490],{"className":3491,"style":873},[767],[574,3493,3495],{"className":3494},[617,1873],[574,3496,1833],{"className":3497},[617],[574,3499],{"className":3500,"style":768},[767],[574,3502,2452],{"className":3503},[772],[574,3505],{"className":3506,"style":768},[767],[574,3508,3510,3513,3517,3523,3527,3530],{"className":3509},[608],[574,3511],{"className":3512,"style":2579},[612],[574,3514,3516],{"className":3515},[617],"10",[574,3518,3520],{"className":3519},[617],[574,3521,2590],{"className":3522},[2589],[574,3524,3526],{"className":3525},[617],"44",[574,3528],{"className":3529,"style":873},[767],[574,3531,3533],{"className":3532},[617,1873],[574,3534,1833],{"className":3535},[617],[565,3537,3538,3539,1877,3604,619,3668,3732,3733,3761],{},"Ein Dreieck hat die Seiten ",[574,3540,3542,3565],{"className":3541},[577],[574,3543,3545],{"className":3544},[581],[583,3546,3547],{"xmlns":585},[587,3548,3549,3562],{},[590,3550,3551,3553,3555,3558,3560],{},[593,3552,595],{},[736,3554,738],{},[743,3556,3557],{},"4",[1828,3559,1830],{},[1828,3561,1833],{},[597,3563,3564],{"encoding":599},"a = 4\\,\\text{cm}",[574,3566,3568,3586],{"className":3567,"ariaHidden":604},[603],[574,3569,3571,3574,3577,3580,3583],{"className":3570},[608],[574,3572],{"className":3573,"style":613},[612],[574,3575,595],{"className":3576},[617,618],[574,3578],{"className":3579,"style":768},[767],[574,3581,738],{"className":3582},[772],[574,3584],{"className":3585,"style":768},[767],[574,3587,3589,3592,3595,3598],{"className":3588},[608],[574,3590],{"className":3591,"style":892},[612],[574,3593,3557],{"className":3594},[617],[574,3596],{"className":3597,"style":873},[767],[574,3599,3601],{"className":3600},[617,1873],[574,3602,1833],{"className":3603},[617],[574,3605,3607,3629],{"className":3606},[577],[574,3608,3610],{"className":3609},[581],[583,3611,3612],{"xmlns":585},[587,3613,3614,3626],{},[590,3615,3616,3618,3620,3622,3624],{},[593,3617,634],{},[736,3619,738],{},[743,3621,1826],{},[1828,3623,1830],{},[1828,3625,1833],{},[597,3627,3628],{"encoding":599},"b = 5\\,\\text{cm}",[574,3630,3632,3650],{"className":3631,"ariaHidden":604},[603],[574,3633,3635,3638,3641,3644,3647],{"className":3634},[608],[574,3636],{"className":3637,"style":646},[612],[574,3639,634],{"className":3640},[617,618],[574,3642],{"className":3643,"style":768},[767],[574,3645,738],{"className":3646},[772],[574,3648],{"className":3649,"style":768},[767],[574,3651,3653,3656,3659,3662],{"className":3652},[608],[574,3654],{"className":3655,"style":892},[612],[574,3657,1826],{"className":3658},[617],[574,3660],{"className":3661,"style":873},[767],[574,3663,3665],{"className":3664},[617,1873],[574,3666,1833],{"className":3667},[617],[574,3669,3671,3693],{"className":3670},[577],[574,3672,3674],{"className":3673},[581],[583,3675,3676],{"xmlns":585},[587,3677,3678,3690],{},[590,3679,3680,3682,3684,3686,3688],{},[593,3681,702],{},[736,3683,738],{},[743,3685,2000],{},[1828,3687,1830],{},[1828,3689,1833],{},[597,3691,3692],{"encoding":599},"c = 6\\,\\text{cm}",[574,3694,3696,3714],{"className":3695,"ariaHidden":604},[603],[574,3697,3699,3702,3705,3708,3711],{"className":3698},[608],[574,3700],{"className":3701,"style":613},[612],[574,3703,702],{"className":3704},[617,618],[574,3706],{"className":3707,"style":768},[767],[574,3709,738],{"className":3710},[772],[574,3712],{"className":3713,"style":768},[767],[574,3715,3717,3720,3723,3726],{"className":3716},[608],[574,3718],{"className":3719,"style":892},[612],[574,3721,2000],{"className":3722},[617],[574,3724],{"className":3725,"style":873},[767],[574,3727,3729],{"className":3728},[617,1873],[574,3730,1833],{"className":3731},[617],". Gesucht ist der Winkel ",[574,3734,3736,3749],{"className":3735},[577],[574,3737,3739],{"className":3738},[581],[583,3740,3741],{"xmlns":585},[587,3742,3743,3747],{},[590,3744,3745],{},[593,3746,665],{},[597,3748,668],{"encoding":599},[574,3750,3752],{"className":3751,"ariaHidden":604},[603],[574,3753,3755,3758],{"className":3754},[608],[574,3756],{"className":3757,"style":678},[612],[574,3759,665],{"className":3760,"style":682},[617,618]," gegenüber der längsten Seite:",[574,3763,3765],{"className":3764},[1072],[574,3766,3768,3859],{"className":3767},[577],[574,3769,3771],{"className":3770},[581],[583,3772,3773],{"xmlns":585,"display":1081},[587,3774,3775,3856],{},[590,3776,3777,3779,3781,3783,3785,3823,3825,3832,3834,3837,3840,3843,3845,3847,3849],{},[593,3778,844],{},[736,3780,847],{},[593,3782,665],{},[736,3784,738],{},[1548,3786,3787,3811],{},[590,3788,3789,3795,3797,3803,3805],{},[740,3790,3791,3793],{},[743,3792,3557],{},[743,3794,915],{},[736,3796,926],{},[740,3798,3799,3801],{},[743,3800,1826],{},[743,3802,915],{},[736,3804,1110],{},[740,3806,3807,3809],{},[743,3808,2000],{},[743,3810,915],{},[590,3812,3813,3815,3817,3819,3821],{},[743,3814,915],{},[736,3816,1119],{},[743,3818,3557],{},[736,3820,1119],{},[743,3822,1826],{},[736,3824,738],{},[1548,3826,3827,3829],{},[743,3828,1826],{},[743,3830,3831],{},"40",[736,3833,738],{},[743,3835,3836],{},"0,125",[767,3838],{"width":3839},"1em",[736,3841,3842],{},"⇒",[767,3844],{"width":3839},[593,3846,665],{},[736,3848,2452],{},[740,3850,3851,3854],{},[743,3852,3853],{},"82,82",[736,3855,748],{},[597,3857,3858],{"encoding":599},"\\cos \\gamma = \\frac{4^2 + 5^2 - 6^2}{2 \\cdot 4 \\cdot 5} = \\frac{5}{40} = 0{,}125\n\\quad\\Rightarrow\\quad\n\\gamma \\approx 82{,}82^\\circ",[574,3860,3862,3886,4089,4168,4203,4222],{"className":3861,"ariaHidden":604},[603],[574,3863,3865,3868,3871,3874,3877,3880,3883],{"className":3864},[608],[574,3866],{"className":3867,"style":678},[612],[574,3869,844],{"className":3870},[869],[574,3872],{"className":3873,"style":873},[767],[574,3875,665],{"className":3876,"style":682},[617,618],[574,3878],{"className":3879,"style":768},[767],[574,3881,738],{"className":3882},[772],[574,3884],{"className":3885,"style":768},[767],[574,3887,3889,3892,4080,4083,4086],{"className":3888},[608],[574,3890],{"className":3891,"style":1618},[612],[574,3893,3895,3898,4077],{"className":3894},[617],[574,3896],{"className":3897},[1625,1626],[574,3899,3901],{"className":3900},[1548],[574,3902,3904,4069],{"className":3903},[801,1633],[574,3905,3907,4066],{"className":3906},[805],[574,3908,3910,3945,3953],{"className":3909,"style":1640},[809],[574,3911,3912,3915],{"style":1643},[574,3913],{"className":3914,"style":1647},[816],[574,3916,3918,3921,3924,3927,3930,3933,3936,3939,3942],{"className":3917},[617],[574,3919,915],{"className":3920},[617],[574,3922],{"className":3923,"style":1023},[767],[574,3925,1119],{"className":3926},[828],[574,3928],{"className":3929,"style":1023},[767],[574,3931,3557],{"className":3932},[617],[574,3934],{"className":3935,"style":1023},[767],[574,3937,1119],{"className":3938},[828],[574,3940],{"className":3941,"style":1023},[767],[574,3943,1826],{"className":3944},[617],[574,3946,3947,3950],{"style":1660},[574,3948],{"className":3949,"style":1647},[816],[574,3951],{"className":3952,"style":1668},[1667],[574,3954,3955,3958],{"style":1671},[574,3956],{"className":3957,"style":1647},[816],[574,3959,3961,3990,3993,3996,3999,4028,4031,4034,4037],{"className":3960},[617],[574,3962,3964,3967],{"className":3963},[617],[574,3965,3557],{"className":3966},[617],[574,3968,3970],{"className":3969},[797],[574,3971,3973],{"className":3972},[801],[574,3974,3976],{"className":3975},[805],[574,3977,3979],{"className":3978,"style":945},[809],[574,3980,3981,3984],{"style":812},[574,3982],{"className":3983,"style":817},[816],[574,3985,3987],{"className":3986},[821,822,823,824],[574,3988,915],{"className":3989},[617,824],[574,3991],{"className":3992,"style":1023},[767],[574,3994,926],{"className":3995},[828],[574,3997],{"className":3998,"style":1023},[767],[574,4000,4002,4005],{"className":4001},[617],[574,4003,1826],{"className":4004},[617],[574,4006,4008],{"className":4007},[797],[574,4009,4011],{"className":4010},[801],[574,4012,4014],{"className":4013},[805],[574,4015,4017],{"className":4016,"style":945},[809],[574,4018,4019,4022],{"style":812},[574,4020],{"className":4021,"style":817},[816],[574,4023,4025],{"className":4024},[821,822,823,824],[574,4026,915],{"className":4027},[617,824],[574,4029],{"className":4030,"style":1023},[767],[574,4032,1110],{"className":4033},[828],[574,4035],{"className":4036,"style":1023},[767],[574,4038,4040,4043],{"className":4039},[617],[574,4041,2000],{"className":4042},[617],[574,4044,4046],{"className":4045},[797],[574,4047,4049],{"className":4048},[801],[574,4050,4052],{"className":4051},[805],[574,4053,4055],{"className":4054,"style":945},[809],[574,4056,4057,4060],{"style":812},[574,4058],{"className":4059,"style":817},[816],[574,4061,4063],{"className":4062},[821,822,823,824],[574,4064,915],{"className":4065},[617,824],[574,4067,1787],{"className":4068},[1786],[574,4070,4072],{"className":4071},[805],[574,4073,4075],{"className":4074,"style":1794},[809],[574,4076],{},[574,4078],{"className":4079},[1800,1626],[574,4081],{"className":4082,"style":768},[767],[574,4084,738],{"className":4085},[772],[574,4087],{"className":4088,"style":768},[767],[574,4090,4092,4096,4159,4162,4165],{"className":4091},[608],[574,4093],{"className":4094,"style":4095},[612],"height:2.0074em;vertical-align:-0.686em;",[574,4097,4099,4102,4156],{"className":4098},[617],[574,4100],{"className":4101},[1625,1626],[574,4103,4105],{"className":4104},[1548],[574,4106,4108,4148],{"className":4107},[801,1633],[574,4109,4111,4145],{"className":4110},[805],[574,4112,4115,4126,4134],{"className":4113,"style":4114},[809],"height:1.3214em;",[574,4116,4117,4120],{"style":1643},[574,4118],{"className":4119,"style":1647},[816],[574,4121,4123],{"className":4122},[617],[574,4124,3831],{"className":4125},[617],[574,4127,4128,4131],{"style":1660},[574,4129],{"className":4130,"style":1647},[816],[574,4132],{"className":4133,"style":1668},[1667],[574,4135,4136,4139],{"style":1671},[574,4137],{"className":4138,"style":1647},[816],[574,4140,4142],{"className":4141},[617],[574,4143,1826],{"className":4144},[617],[574,4146,1787],{"className":4147},[1786],[574,4149,4151],{"className":4150},[805],[574,4152,4154],{"className":4153,"style":1794},[809],[574,4155],{},[574,4157],{"className":4158},[1800,1626],[574,4160],{"className":4161,"style":768},[767],[574,4163,738],{"className":4164},[772],[574,4166],{"className":4167,"style":768},[767],[574,4169,4171,4174,4177,4183,4187,4191,4194,4197,4200],{"className":4170},[608],[574,4172],{"className":4173,"style":2579},[612],[574,4175,793],{"className":4176},[617],[574,4178,4180],{"className":4179},[617],[574,4181,2590],{"className":4182},[2589],[574,4184,4186],{"className":4185},[617],"125",[574,4188],{"className":4189,"style":4190},[767],"margin-right:1em;",[574,4192],{"className":4193,"style":768},[767],[574,4195,3842],{"className":4196},[772],[574,4198],{"className":4199,"style":4190},[767],[574,4201],{"className":4202,"style":768},[767],[574,4204,4206,4210,4213,4216,4219],{"className":4205},[608],[574,4207],{"className":4208,"style":4209},[612],"height:0.6776em;vertical-align:-0.1944em;",[574,4211,665],{"className":4212,"style":682},[617,618],[574,4214],{"className":4215,"style":768},[767],[574,4217,2452],{"className":4218},[772],[574,4220],{"className":4221,"style":768},[767],[574,4223,4225,4229,4233,4239,4243],{"className":4224},[608],[574,4226],{"className":4227,"style":4228},[612],"height:0.9186em;vertical-align:-0.1944em;",[574,4230,4232],{"className":4231},[617],"82",[574,4234,4236],{"className":4235},[617],[574,4237,2590],{"className":4238},[2589],[574,4240,4242],{"className":4241},[617],"8",[574,4244,4246,4249],{"className":4245},[617],[574,4247,915],{"className":4248},[617],[574,4250,4252],{"className":4251},[797],[574,4253,4255],{"className":4254},[801],[574,4256,4258],{"className":4257},[805],[574,4259,4261],{"className":4260,"style":2310},[809],[574,4262,4263,4266],{"style":1202},[574,4264],{"className":4265,"style":817},[816],[574,4267,4269],{"className":4268},[821,822,823,824],[574,4270,748],{"className":4271},[828,824],[560,4273,4275],{"id":4274},"typische-fehler","Typische Fehler",[4277,4278,4279,4402,4835,4925],"ul",{},[4280,4281,4282,4283,619,4311,4339,4340,4368,4369,4372,4373,4401],"li",{},"Einen Winkel einsetzen, der nicht zwischen ",[574,4284,4286,4299],{"className":4285},[577],[574,4287,4289],{"className":4288},[581],[583,4290,4291],{"xmlns":585},[587,4292,4293,4297],{},[590,4294,4295],{},[593,4296,595],{},[597,4298,595],{"encoding":599},[574,4300,4302],{"className":4301,"ariaHidden":604},[603],[574,4303,4305,4308],{"className":4304},[608],[574,4306],{"className":4307,"style":613},[612],[574,4309,595],{"className":4310},[617,618],[574,4312,4314,4327],{"className":4313},[577],[574,4315,4317],{"className":4316},[581],[583,4318,4319],{"xmlns":585},[587,4320,4321,4325],{},[590,4322,4323],{},[593,4324,634],{},[597,4326,634],{"encoding":599},[574,4328,4330],{"className":4329,"ariaHidden":604},[603],[574,4331,4333,4336],{"className":4332},[608],[574,4334],{"className":4335,"style":646},[612],[574,4337,634],{"className":4338},[617,618]," liegt. Im Kosinussatz für ",[574,4341,4343,4356],{"className":4342},[577],[574,4344,4346],{"className":4345},[581],[583,4347,4348],{"xmlns":585},[587,4349,4350,4354],{},[590,4351,4352],{},[593,4353,702],{},[597,4355,702],{"encoding":599},[574,4357,4359],{"className":4358,"ariaHidden":604},[603],[574,4360,4362,4365],{"className":4361},[608],[574,4363],{"className":4364,"style":613},[612],[574,4366,702],{"className":4367},[617,618]," steht immer der Winkel ",[569,4370,4371],{},"gegenüber"," von ",[574,4374,4376,4389],{"className":4375},[577],[574,4377,4379],{"className":4378},[581],[583,4380,4381],{"xmlns":585},[587,4382,4383,4387],{},[590,4384,4385],{},[593,4386,702],{},[597,4388,702],{"encoding":599},[574,4390,4392],{"className":4391,"ariaHidden":604},[603],[574,4393,4395,4398],{"className":4394},[608],[574,4396],{"className":4397,"style":613},[612],[574,4399,702],{"className":4400},[617,618],".",[4280,4403,4404,4405,4577,4578,4765,4766,4834],{},"Rechenreihenfolge: ",[574,4406,4408,4450],{"className":4407},[577],[574,4409,4411],{"className":4410},[581],[583,4412,4413],{"xmlns":585},[587,4414,4415,4447],{},[590,4416,4417,4423,4425,4431,4433,4435,4437,4439,4441,4443,4445],{},[740,4418,4419,4421],{},[593,4420,595],{},[743,4422,915],{},[736,4424,926],{},[740,4426,4427,4429],{},[593,4428,634],{},[743,4430,915],{},[736,4432,1110],{},[743,4434,915],{},[593,4436,595],{},[593,4438,634],{},[736,4440,1119],{},[593,4442,844],{},[736,4444,847],{},[593,4446,665],{},[597,4448,4449],{"encoding":599},"a^2 + b^2 - 2ab \\cdot \\cos \\gamma",[574,4451,4453,4497,4541,4562],{"className":4452,"ariaHidden":604},[603],[574,4454,4456,4459,4488,4491,4494],{"className":4455},[608],[574,4457],{"className":4458,"style":990},[612],[574,4460,4462,4465],{"className":4461},[617],[574,4463,595],{"className":4464},[617,618],[574,4466,4468],{"className":4467},[797],[574,4469,4471],{"className":4470},[801],[574,4472,4474],{"className":4473},[805],[574,4475,4477],{"className":4476,"style":945},[809],[574,4478,4479,4482],{"style":812},[574,4480],{"className":4481,"style":817},[816],[574,4483,4485],{"className":4484},[821,822,823,824],[574,4486,915],{"className":4487},[617,824],[574,4489],{"className":4490,"style":1023},[767],[574,4492,926],{"className":4493},[828],[574,4495],{"className":4496,"style":1023},[767],[574,4498,4500,4503,4532,4535,4538],{"className":4499},[608],[574,4501],{"className":4502,"style":990},[612],[574,4504,4506,4509],{"className":4505},[617],[574,4507,634],{"className":4508},[617,618],[574,4510,4512],{"className":4511},[797],[574,4513,4515],{"className":4514},[801],[574,4516,4518],{"className":4517},[805],[574,4519,4521],{"className":4520,"style":945},[809],[574,4522,4523,4526],{"style":812},[574,4524],{"className":4525,"style":817},[816],[574,4527,4529],{"className":4528},[821,822,823,824],[574,4530,915],{"className":4531},[617,824],[574,4533],{"className":4534,"style":1023},[767],[574,4536,1110],{"className":4537},[828],[574,4539],{"className":4540,"style":1023},[767],[574,4542,4544,4547,4550,4553,4556,4559],{"className":4543},[608],[574,4545],{"className":4546,"style":646},[612],[574,4548,915],{"className":4549},[617],[574,4551,1657],{"className":4552},[617,618],[574,4554],{"className":4555,"style":1023},[767],[574,4557,1119],{"className":4558},[828],[574,4560],{"className":4561,"style":1023},[767],[574,4563,4565,4568,4571,4574],{"className":4564},[608],[574,4566],{"className":4567,"style":678},[612],[574,4569,844],{"className":4570},[869],[574,4572],{"className":4573,"style":873},[767],[574,4575,665],{"className":4576,"style":682},[617,618]," ist nicht ",[574,4579,4581,4630],{"className":4580},[577],[574,4582,4584],{"className":4583},[581],[583,4585,4586],{"xmlns":585},[587,4587,4588,4627],{},[590,4589,4590,4594,4600,4602,4608,4610,4612,4614,4616,4619,4621,4623,4625],{},[736,4591,4593],{"stretchy":4592},"false","(",[740,4595,4596,4598],{},[593,4597,595],{},[743,4599,915],{},[736,4601,926],{},[740,4603,4604,4606],{},[593,4605,634],{},[743,4607,915],{},[736,4609,1110],{},[743,4611,915],{},[593,4613,595],{},[593,4615,634],{},[736,4617,4618],{"stretchy":4592},")",[736,4620,1119],{},[593,4622,844],{},[736,4624,847],{},[593,4626,665],{},[597,4628,4629],{"encoding":599},"(a^2 + b^2 - 2ab) \\cdot \\cos \\gamma",[574,4631,4633,4681,4725,4750],{"className":4632,"ariaHidden":604},[603],[574,4634,4636,4640,4643,4672,4675,4678],{"className":4635},[608],[574,4637],{"className":4638,"style":4639},[612],"height:1.0641em;vertical-align:-0.25em;",[574,4641,4593],{"className":4642},[1625],[574,4644,4646,4649],{"className":4645},[617],[574,4647,595],{"className":4648},[617,618],[574,4650,4652],{"className":4651},[797],[574,4653,4655],{"className":4654},[801],[574,4656,4658],{"className":4657},[805],[574,4659,4661],{"className":4660,"style":945},[809],[574,4662,4663,4666],{"style":812},[574,4664],{"className":4665,"style":817},[816],[574,4667,4669],{"className":4668},[821,822,823,824],[574,4670,915],{"className":4671},[617,824],[574,4673],{"className":4674,"style":1023},[767],[574,4676,926],{"className":4677},[828],[574,4679],{"className":4680,"style":1023},[767],[574,4682,4684,4687,4716,4719,4722],{"className":4683},[608],[574,4685],{"className":4686,"style":990},[612],[574,4688,4690,4693],{"className":4689},[617],[574,4691,634],{"className":4692},[617,618],[574,4694,4696],{"className":4695},[797],[574,4697,4699],{"className":4698},[801],[574,4700,4702],{"className":4701},[805],[574,4703,4705],{"className":4704,"style":945},[809],[574,4706,4707,4710],{"style":812},[574,4708],{"className":4709,"style":817},[816],[574,4711,4713],{"className":4712},[821,822,823,824],[574,4714,915],{"className":4715},[617,824],[574,4717],{"className":4718,"style":1023},[767],[574,4720,1110],{"className":4721},[828],[574,4723],{"className":4724,"style":1023},[767],[574,4726,4728,4732,4735,4738,4741,4744,4747],{"className":4727},[608],[574,4729],{"className":4730,"style":4731},[612],"height:1em;vertical-align:-0.25em;",[574,4733,915],{"className":4734},[617],[574,4736,1657],{"className":4737},[617,618],[574,4739,4618],{"className":4740},[1800],[574,4742],{"className":4743,"style":1023},[767],[574,4745,1119],{"className":4746},[828],[574,4748],{"className":4749,"style":1023},[767],[574,4751,4753,4756,4759,4762],{"className":4752},[608],[574,4754],{"className":4755,"style":678},[612],[574,4757,844],{"className":4758},[869],[574,4760],{"className":4761,"style":873},[767],[574,4763,665],{"className":4764,"style":682},[617,618],". Erst das Produkt ",[574,4767,4769,4795],{"className":4768},[577],[574,4770,4772],{"className":4771},[581],[583,4773,4774],{"xmlns":585},[587,4775,4776,4792],{},[590,4777,4778,4780,4782,4784,4786,4788,4790],{},[743,4779,915],{},[593,4781,595],{},[593,4783,634],{},[736,4785,1119],{},[593,4787,844],{},[736,4789,847],{},[593,4791,665],{},[597,4793,4794],{"encoding":599},"2ab \\cdot \\cos \\gamma",[574,4796,4798,4819],{"className":4797,"ariaHidden":604},[603],[574,4799,4801,4804,4807,4810,4813,4816],{"className":4800},[608],[574,4802],{"className":4803,"style":646},[612],[574,4805,915],{"className":4806},[617],[574,4808,1657],{"className":4809},[617,618],[574,4811],{"className":4812,"style":1023},[767],[574,4814,1119],{"className":4815},[828],[574,4817],{"className":4818,"style":1023},[767],[574,4820,4822,4825,4828,4831],{"className":4821},[608],[574,4823],{"className":4824,"style":678},[612],[574,4826,844],{"className":4827},[869],[574,4829],{"className":4830,"style":873},[767],[574,4832,665],{"className":4833,"style":682},[617,618]," bilden, dann abziehen.",[4280,4836,4837,4838,4896,4897,4401],{},"Am Ende die Wurzel vergessen: Die Formel liefert ",[574,4839,4841,4858],{"className":4840},[577],[574,4842,4844],{"className":4843},[581],[583,4845,4846],{"xmlns":585},[587,4847,4848,4856],{},[590,4849,4850],{},[740,4851,4852,4854],{},[593,4853,702],{},[743,4855,915],{},[597,4857,2950],{"encoding":599},[574,4859,4861],{"className":4860,"ariaHidden":604},[603],[574,4862,4864,4867],{"className":4863},[608],[574,4865],{"className":4866,"style":945},[612],[574,4868,4870,4873],{"className":4869},[617],[574,4871,702],{"className":4872},[617,618],[574,4874,4876],{"className":4875},[797],[574,4877,4879],{"className":4878},[801],[574,4880,4882],{"className":4881},[805],[574,4883,4885],{"className":4884,"style":945},[809],[574,4886,4887,4890],{"style":812},[574,4888],{"className":4889,"style":817},[816],[574,4891,4893],{"className":4892},[821,822,823,824],[574,4894,915],{"className":4895},[617,824],", nicht ",[574,4898,4900,4913],{"className":4899},[577],[574,4901,4903],{"className":4902},[581],[583,4904,4905],{"xmlns":585},[587,4906,4907,4911],{},[590,4908,4909],{},[593,4910,702],{},[597,4912,702],{"encoding":599},[574,4914,4916],{"className":4915,"ariaHidden":604},[603],[574,4917,4919,4922],{"className":4918},[608],[574,4920],{"className":4921,"style":613},[612],[574,4923,702],{"className":4924},[617,618],[4280,4926,4927,4928,4956,4957,4996,4997,5055,5056,4401],{},"Bei stumpfem ",[574,4929,4931,4944],{"className":4930},[577],[574,4932,4934],{"className":4933},[581],[583,4935,4936],{"xmlns":585},[587,4937,4938,4942],{},[590,4939,4940],{},[593,4941,665],{},[597,4943,668],{"encoding":599},[574,4945,4947],{"className":4946,"ariaHidden":604},[603],[574,4948,4950,4953],{"className":4949},[608],[574,4951],{"className":4952,"style":678},[612],[574,4954,665],{"className":4955,"style":682},[617,618]," das Vorzeichen übersehen: ",[574,4958,4960,4978],{"className":4959},[577],[574,4961,4963],{"className":4962},[581],[583,4964,4965],{"xmlns":585},[587,4966,4967,4975],{},[590,4968,4969,4971,4973],{},[593,4970,844],{},[736,4972,847],{},[593,4974,665],{},[597,4976,4977],{"encoding":599},"\\cos \\gamma",[574,4979,4981],{"className":4980,"ariaHidden":604},[603],[574,4982,4984,4987,4990,4993],{"className":4983},[608],[574,4985],{"className":4986,"style":678},[612],[574,4988,844],{"className":4989},[869],[574,4991],{"className":4992,"style":873},[767],[574,4994,665],{"className":4995,"style":682},[617,618]," ist dann negativ, und ",[574,4998,5000,5017],{"className":4999},[577],[574,5001,5003],{"className":5002},[581],[583,5004,5005],{"xmlns":585},[587,5006,5007,5015],{},[590,5008,5009],{},[740,5010,5011,5013],{},[593,5012,702],{},[743,5014,915],{},[597,5016,2950],{"encoding":599},[574,5018,5020],{"className":5019,"ariaHidden":604},[603],[574,5021,5023,5026],{"className":5022},[608],[574,5024],{"className":5025,"style":945},[612],[574,5027,5029,5032],{"className":5028},[617],[574,5030,702],{"className":5031},[617,618],[574,5033,5035],{"className":5034},[797],[574,5036,5038],{"className":5037},[801],[574,5039,5041],{"className":5040},[805],[574,5042,5044],{"className":5043,"style":945},[809],[574,5045,5046,5049],{"style":812},[574,5047],{"className":5048,"style":817},[816],[574,5050,5052],{"className":5051},[821,822,823,824],[574,5053,915],{"className":5054},[617,824]," wird größer als ",[574,5057,5059,5085],{"className":5058},[577],[574,5060,5062],{"className":5061},[581],[583,5063,5064],{"xmlns":585},[587,5065,5066,5082],{},[590,5067,5068,5074,5076],{},[740,5069,5070,5072],{},[593,5071,595],{},[743,5073,915],{},[736,5075,926],{},[740,5077,5078,5080],{},[593,5079,634],{},[743,5081,915],{},[597,5083,5084],{"encoding":599},"a^2 + b^2",[574,5086,5088,5132],{"className":5087,"ariaHidden":604},[603],[574,5089,5091,5094,5123,5126,5129],{"className":5090},[608],[574,5092],{"className":5093,"style":990},[612],[574,5095,5097,5100],{"className":5096},[617],[574,5098,595],{"className":5099},[617,618],[574,5101,5103],{"className":5102},[797],[574,5104,5106],{"className":5105},[801],[574,5107,5109],{"className":5108},[805],[574,5110,5112],{"className":5111,"style":945},[809],[574,5113,5114,5117],{"style":812},[574,5115],{"className":5116,"style":817},[816],[574,5118,5120],{"className":5119},[821,822,823,824],[574,5121,915],{"className":5122},[617,824],[574,5124],{"className":5125,"style":1023},[767],[574,5127,926],{"className":5128},[828],[574,5130],{"className":5131,"style":1023},[767],[574,5133,5135,5138],{"className":5134},[608],[574,5136],{"className":5137,"style":945},[612],[574,5139,5141,5144],{"className":5140},[617],[574,5142,634],{"className":5143},[617,618],[574,5145,5147],{"className":5146},[797],[574,5148,5150],{"className":5149},[801],[574,5151,5153],{"className":5152},[805],[574,5154,5156],{"className":5155,"style":945},[809],[574,5157,5158,5161],{"style":812},[574,5159],{"className":5160,"style":817},[816],[574,5162,5164],{"className":5163},[821,822,823,824],[574,5165,915],{"className":5166},[617,824],{"title":5168,"searchDepth":5169,"depth":5169,"links":5170},"",2,[5171,5172,5173],{"id":562,"depth":5169,"text":563},{"id":1803,"depth":5169,"text":1804},{"id":4274,"depth":5169,"text":4275},[5175,5178,5180,5182,5185,5188,5190,5193,5196,5199],{"lhs":5176,"rhs":5177},"(a*cos(x) - b)^2 + (a*sin(x))^2","a^2 + b^2 - 2*a*b*cos(x)",{"lhs":5179,"rhs":5084},"a^2 + b^2 - 2*a*b*cos(pi\u002F2)",{"lhs":5181,"rhs":2111},"5^2 + 7^2 - 2*5*7*cos(60*pi\u002F180)",{"lhs":5183,"rhs":5184},"round(sqrt(39), 2)","6.24",{"lhs":5186,"rhs":5187},"cos(120*pi\u002F180)","-0.5",{"lhs":5189,"rhs":3067},"5^2 + 7^2 - 2*5*7*cos(120*pi\u002F180)",{"lhs":5191,"rhs":5192},"2*5*7*cos(120*pi\u002F180)","-35",{"lhs":5194,"rhs":5195},"round(sqrt(109), 2)","10.44",{"lhs":5197,"rhs":5198},"(4^2 + 5^2 - 6^2) \u002F (2*4*5)","0.125",{"lhs":5200,"rhs":5201},"round(acos(0.125) * 180\u002Fpi, 2)","82.82","\\text{beliebiges Dreieck};\\ \\gamma\\ \\text{ist der Winkel zwischen}\\ a\\ \\text{und}\\ b","\u003Cspan class=\"katex\">beliebiges\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Dreieck\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">;\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">;\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">ist der Winkel zwischen\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":5207,"x":5208,"y":5211,"unit":5214,"items":5215},"Dreieck mit den Seiten a und b, die den Winkel γ einschließen, und der gegenüberliegenden Seite c",[5209,5210],-0.8,7.9,[5212,5213],-0.9,5,34,[5216,5228,5232,5237,5242,5246,5250,5257,5262],{"type":5217,"points":5218,"fill":5226,"style":5227},"polygon",[5219,5222,5225],[5220,5221],7,0,[5223,5224],2.5,4.33,[5221,5221],true,"muted",{"type":5229,"from":5230,"to":5231},"segment",[5220,5221],[5223,5224],{"type":5233,"at":5234,"from":5235,"to":5236,"label":665},"angle",[5221,5221],[5220,5221],[5223,5224],{"type":5238,"at":5239,"text":595},"label",[5240,5241],0.86,2.39,{"type":5238,"at":5243,"text":634},[5244,5245],3.5,-0.45,{"type":5238,"at":5247,"text":702},[5248,5249],5.06,2.49,{"type":5251,"at":5252,"label":5253,"offset":5254},"point",[5220,5221],"A",[5255,5256],6,10,{"type":5251,"at":5258,"label":5259,"offset":5260},[5223,5224],"B",[5255,5261],-10,{"type":5251,"at":5263,"label":5264,"offset":5265},[5221,5221],"C",[5266,5256],-18,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 295.8 200.6\" width=\"295.8\" height=\"200.6\" role=\"img\" aria-label=\"Dreieck mit den Seiten a und b, die den Winkel γ einschließen, und der gegenüberliegenden Seite c\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-law-of-cosines-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-cosines-clip\">\u003Crect x=\"0\" y=\"0\" width=\"295.8\" height=\"200.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"265.2,170 112.2,22.78 27.2,170\" class=\"fig-muted fig-fill\"\u002F>\u003Cline x1=\"265.2\" y1=\"170\" x2=\"112.2\" y2=\"22.78\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 27.2 170 L 49.2 170 A 22 22 0 0 0 38.2 150.95 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"56.64\" y=\"153\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">γ\u003C\u002Ftext>\u003Ctext x=\"56.44\" y=\"88.74\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"146.2\" y=\"185.3\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"199.24\" y=\"85.34\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ccircle cx=\"265.2\" cy=\"170\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"271.2\" y=\"180\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"112.2\" cy=\"22.78\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.2\" y=\"12.780000000000001\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"27.2\" cy=\"170\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"9.2\" y=\"180\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","law-of-cosines","c^2 = a^2 + b^2 - 2ab \\cdot \\cos \\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>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c^2 = a^2 + b^2 - 2ab \\cdot \\cos \\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">ab\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=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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