d = 8/sin(30°) = 16d = x/sin(45°) = 16x = 16*sin(45°) = 16/√2 = 8√2y = 16*sin(180-45-30) = 16*sin(105°)неудобный угол. поищем решение в радикалахsin(105°) = cos(15°)cos²(α/2) = (1+cos(α))/2cos²(15°) = (1+cos(30°))/2 = (1+√3/2)/2 = 1/2+√3/4cos(15°) = √(1/2+√3/4) 1/2+√3/4 = (a+b√3)² = a²+3b² + 2ab√3√3/4 = 2ab√3ab = 1/8a = 1/(8b)1/2 = a²+3b² = 1/(64*b²) +3b²192b⁴ + 1 = 32b²192b⁴ - 32b² + 1 = 0t = b²192t² - 32t + 1 = 0t₁ = (32-√(32²-4*192))/(2*192) = (32-√256)/384 = 16/384 = 1/24b₁ = -1/(2√6)b₂ = 1/(2√6)t₂ = (32+√(32²-4*192))/(2*192) = (32+16)/384 = 1/8b₃ = -1/(2√2)b₄ = 1/(2√2)используем последний кореньb = 1/(2√2)a = 2√2/8 = 1/(2√2)1/2+√3/4 = (a+b√3)² = (1/(2√2) + 1/(2√2)*√3)² cos(15°) = √(1/2+√3/4) = 1/(2√2) + 1/(2√2)*√3 = 1/4(√2+√3)y = 16*cos(15°) = 4(√2+√3)-------------∠R = 180-80 = 100°∠M = 180-100-50 = 30°снова по теореме синусов диаметр описанной окружностиd = 13/sin(30°) = 26x = 26*sin(50°) ≈ 19,92y = 26*sin(100°) ≈ 25,61