Предмет: Математика, автор: sanyytixan

До площини α проведена похила, довжина якої дорівнює 15 см, проекція похилої дорівнює 9 см. На якій відстані від площини знаходиться точка, з якої проведена похила?

Точка знаходиться на відстані см?

Ответы

Автор ответа: Vsevishnya

1

Ответ:

12 cm

Пошаговое объяснение:

Позначу вершину похилої як А, а точку перетену похилої до площинии - B, тоді проведемо перпендикулярний відрізок від точки а до площини і позначимо як С, тоді :

ABC = прям. трикутник(бо ми його так провели)

Із задачі беремо сторони нашого трикутника:
(сама похила)AB = 15 cm
(проекція)BC = 9 cm

в задачі треба найти відстань від точку з якої провели похилу, а саме наш перпендикуляр: CB

По теоремі піфагора:

CB = $\sqrt{15^2 - 9^2}$ = 12 cm

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