Question

Решить треугольник MNK, если KM=5м, уголМ=60 градусов, NK=6м

Answer 1

По теореме синусов
2R = NK/sin(∠M) = 6/sin(60°) = 6*2/√3 = 4√3 м
2R = KM/sin(∠N)
sin(∠N) = KM/(2R) = 5/(4√3)
∠N = arcsin(5/(4√3)) ≈ 46,19°
∠K = 180 - ∠M - ∠N = 120 - arcsin(5/(4√3)) ≈ 73,81°
2R = MN/sin(∠K)
MN = 2R*sin(∠K) = 4√3/sin(120 - arcsin(5/(4√3))) ≈ 6,653 м