Question

В треугольнике АВС  АВ=8$\sqrt{3}$ , ВС=7$\sqrt{3}$ , .угол B = 120
Найдите радиус R описанной окружности.

Answer 1

S(ABC) = (1/2) * AB * BC * sin(ABC)
S(ABC) = AB*BC*CA / (4R)
CA² = AB² + BC² - 2*AB*BC*cos(ABC)
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S(ABC) = 8√3 * 7√3 * √3 / 4 = 42√3
CA² = 64*3 + 49*3 - 2*8*7*3*(-1/2)
CA² = 3*(113+56) = 3*13²
4R = 8√3 * 7√3 * 13√3 / (42√3)
4R = 8*7*3*13 / (2*3*7) = 4*13
R = 13