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Консультация № 57594
03.10.2006, 17:53
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Помогите пожалуйста решить задачу, очень надо
Прямая, лежащая в одной из двух пересекающихся плоскостей, образует с линией пересечения этих плоскостей угол альфа. Найти угол между плоскостями, если указанная прямая образует со второй плоскостью угол бета
Заранее большое спасибо.
Прямая, лежащая в одной из двух пересекающихся плоскостей, образует с линией пересечения этих плоскостей угол альфа. Найти угол между плоскостями, если указанная прямая образует со второй плоскостью угол бета
Заранее большое спасибо.
Обсуждение
Неизвестный
03.10.2006, 18:10
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это ответ
Здравствуйте, Сергей Сергеевич Сергеев!
пусть прямая лежит в плоскости альфа и пересекает вторую плоскость(бета)в точке А на ребре получившегося двугранного угла. Отметим на прямой некоторую точку О и из нее опустим перпендикуляр ОВ к ребру двугранного угла и ОН - перпендикуляр к плоскости бета. Тогда по условию угол ОАВ равен альфа, а угол ОАН равен бета. ОВ=ОА*sin(альфа); ОН=АО*sin(бета), sinОВН=ОН/ОВ=sin(бета)/sin(альфа). А сам угол ОВН=arcsin(sin(бета)/sin(альфа)).
пусть прямая лежит в плоскости альфа и пересекает вторую плоскость(бета)в точке А на ребре получившегося двугранного угла. Отметим на прямой некоторую точку О и из нее опустим перпендикуляр ОВ к ребру двугранного угла и ОН - перпендикуляр к плоскости бета. Тогда по условию угол ОАВ равен альфа, а угол ОАН равен бета. ОВ=ОА*sin(альфа); ОН=АО*sin(бета), sinОВН=ОН/ОВ=sin(бета)/sin(альфа). А сам угол ОВН=arcsin(sin(бета)/sin(альфа)).
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