Задание 9, стр 60

Question

Проекции сторон равностороннего треугольника ABC на плоскость $\alpha$ образуют прямоугольный треугольник BDC. Найдите DC, если AC = 8 см.

Gimli · Accepted Answer

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Так как АС = АВ = 8 см, можно заключить, что и проекции этих отрезков на плоскость $\alpha$ равны. Тогда, имеем, что прямоугольный треугольник ДСВ еще и равнобедренный. Отсюда следует (из Теоремы Пифагора), что $CB=x\sqrt{2}.$ Так как треугольник АВС является равносторонним, имеем, что $BC=AC$ и $x\sqrt{2}=8$, а значит, $x=4\sqrt{2}.$ Так как ДС тоже равно х, получаем следующий ответ:
ewline
	extbf{Ответ: $DC=4\sqrt{2}$.}

Задание 9, стр 60

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Задание 9, стр 60

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