По теореме синусов
AB/sin(∠C) = BC/sin(∠A) = AC/sin(∠B)
AB/sin(∠C) = 10/sin(45°) = 10√2
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BC/sin(∠A) = 10√2
BC = 10√2 * sin(60°) = 10√2 * √3/2 = 5√6
x = 5√6
∠B = 180° - ∠A - ∠C = 180 - 60 - 45 = 75°
Понятна трудность, синус 75° :)
sin(75°) = sin(45 + 30) = sin(45°)*cos(30°) + cos(45°)*sin(30°) = 1/√2 * (√3/2 + 1/2) = (√3 +1)/(2√2)
AC/sin(∠B) = 10√2
AC = 10√2 * sin(∠B) = 10√2 * sin(75°) = 10√2 * (√3 +1)/(2√2) = 5(√3 + 1) = 5√3 + 5
y = 5√3 + 5
По теореме синусов
AB/sin(∠C) = BC/sin(∠A) = AC/sin(∠B)
AB/sin(∠C) = 10/sin(45°) = 10√2
---
BC/sin(∠A) = 10√2
BC = 10√2 * sin(60°) = 10√2 * √3/2 = 5√6
x = 5√6
---
∠B = 180° - ∠A - ∠C = 180 - 60 - 45 = 75°
Понятна трудность, синус 75° :)
sin(75°) = sin(45 + 30) = sin(45°)*cos(30°) + cos(45°)*sin(30°) = 1/√2 * (√3/2 + 1/2) = (√3 +1)/(2√2)
---
AC/sin(∠B) = 10√2
AC = 10√2 * sin(∠B) = 10√2 * sin(75°) = 10√2 * (√3 +1)/(2√2) = 5(√3 + 1) = 5√3 + 5
y = 5√3 + 5