Question

Известно 3 стороны треугольника. Найдите его углы, если а=7 b=2 c=8​

Answer 1

Ответ:

113,1323964, 13,2911772, 53,5764264

Объяснение:

$a^{2} =b^{2} +c^{2} -2bccos\alpha \\ 2bccos\alpha = b^{2} +c^{2}-a^{2} \\cos\alpha = \frac{b^{2} + c^{2} - a^{2}}{2bc} \\\alpha = arccos\frac{b^{2} + c^{2} - a^{2}}{2bc} \\a= arccos\frac{19}{32} =arccos0,59375 = 53,5764264\\\\b^{2} =a^{2} +c^{2} -2accos\beta \\ 2bccos\beta = a^{2} +c^{2}-b^{2} \\cos\beta = \frac{a^{2} + c^{2} - b^{2}}{2ac} \\\beta = arccos\frac{a^{2} + c^{2} - b^{2}}{2ac} \\\beta = arccos\frac{109}{112} =arccos0,97321428571428571428 = 13,2911772$

$c=180-\alpha -\beta =113,1323964$