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Консультация № 161092
21.02.2009, 21:32
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Ув. эксперты, помогите справиться с задачей:
Двугранный угол равняется 45 градусов. На одной из его граней дано точку, которая находится на расстоянии sqrt(128) см от другой грани. Найти расстояние от этой точки до ребра угла.
Заранее огромное спасибо!
Двугранный угол равняется 45 градусов. На одной из его граней дано точку, которая находится на расстоянии sqrt(128) см от другой грани. Найти расстояние от этой точки до ребра угла.
Заранее огромное спасибо!
Обсуждение
Неизвестный
21.02.2009, 23:30
общий
это ответ
Здравствуйте, Kafka!
Помогаю :)
Пусть А указанная в условии точка. Опустим перпендикуляр к противоположной грани, который пересечет ее в точке О.Полученный отрезок АО по определению есть расстояние от точки А до другой грани, т.е. АО = sqrt(128). Проведем отрезок AM, перпендикулярный ребру заданного двугранного угла (это есть искомое расстояние от точки А до ребра угла) . Тогда ОМ есть проекция отрезка АМ на противоположную грань, и ОМ также перпендикулярен ребру заданного двугранного угла. По определению АМО есть плоский угол заданного двугранного угла, а значит АМО = 45 градусов.
Рассмотрим треугольник АОМ. Он прямоугольный по построению, угол АМО = 45 градусов, АО = sqrt(128). ТОгда АМ = AO/sin(45 градусов) = sqrt(128)/(1/sqrt(2)) = sqrt(128)*sqrt(2) = sqrt(256) = 16.
Т.е. искомое расстояние от точки А до ребра угла равно 16.
К сожалению, не имею технической возможности привести здесь чертеж, но из описания должно быть все понятно.
Рад был помочь.
Помогаю :)
Пусть А указанная в условии точка. Опустим перпендикуляр к противоположной грани, который пересечет ее в точке О.Полученный отрезок АО по определению есть расстояние от точки А до другой грани, т.е. АО = sqrt(128). Проведем отрезок AM, перпендикулярный ребру заданного двугранного угла (это есть искомое расстояние от точки А до ребра угла) . Тогда ОМ есть проекция отрезка АМ на противоположную грань, и ОМ также перпендикулярен ребру заданного двугранного угла. По определению АМО есть плоский угол заданного двугранного угла, а значит АМО = 45 градусов.
Рассмотрим треугольник АОМ. Он прямоугольный по построению, угол АМО = 45 градусов, АО = sqrt(128). ТОгда АМ = AO/sin(45 градусов) = sqrt(128)/(1/sqrt(2)) = sqrt(128)*sqrt(2) = sqrt(256) = 16.
Т.е. искомое расстояние от точки А до ребра угла равно 16.
К сожалению, не имею технической возможности привести здесь чертеж, но из описания должно быть все понятно.
Рад был помочь.
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