Question

Теорема синусов, пожааааалуйста, помогииите, осталось немного времени

Answer 1

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