Предмет: Математика, автор: angei100

в основании прямой призмы
ABCA1B1C1 лежит равнобедренный тоеугольник abc в котором ab равен bc равен 20 , ac равен 24, b1c равен 30. найдите синус угла наклона b1c к грани aa1c1c помогите пожалуйста)

Ответы

Автор ответа: Аноним

0

Дано:
ABCA₁B₁C₁ - прямая призма
AB=BC=20
AC=24
B₁C=30
Найти: sinα
Решение:
Угол между прямой и плоскостью - это угол между ней и ее проекцией на эту плоскость. Проекцией B₁C является DC, где D - середина A₁C₁ (т.к. треугольник в основании равнобедренный). По т.Пифагора находим B₁D
B₁D=√(B₁C₁²-(0.5A₁C₁)²=√(20²-12²)=16
По определению синуса
sinα=B₁D/B₁C=16/30=8/15
Ответ: 8/15

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