По теореме осинусов
c² = 100² + 500² - 2*100*500*cos(10°) = 260000 - 100000 cos(10°)
c = √(260000 - 100000 cos(10°)) ≈ 401,9
по теореме синусов
2R = c/sin(∠C) = √(260000 - 100000 cos(10°))/sin(10°) ≈ 2314
sin(∠A) = a/(2R) = 100/2314 ≈ 0.04321
∠A = arcsin(100/(√(260000 - 100000 cos(10°))/sin(10°))) = 2,476°
sin(∠B) = b/(2R) = 500/2314 ≈ 0,216
∠B = arcsin(500/(√(260000 - 100000 cos(10°))/sin(10°))) = 12,48°