Предмет: Геометрия, автор: mandydaniel

Плоскость а(альфа) проходит через сторону СК квадрата СДЕК(на рисунке он изображён в виде параллелограмма),причём диагональ ДК образует с плоскостью а(альфа) угол, синус которого равен (корень из 2 делёное на 4).

Найти угол,который образует с плоскостью а(альфа) СД.

Ответы

Автор ответа: cos20093
0

если обозначить М - проекция точки D на плоскость альфа, то DM = КD*sin(Ф); (это синус, заданный в задаче). При этом КD = CD*корень(2); (KD - диагональ квадрата, CD - сторона). Отсюда (не забудем, что sin(Ф) = корень(2)/4) получаем DM = CD/2; поэтому угол DCM равен 30 градусам.

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