Предмет: Геометрия, автор: kamila9789

в правильной треугольной пирамиде сторона основания равна 6 корней из 5, а длина бокового ребра равна 16. найдите высоту пирамиды.

Ответы

Автор ответа: Andr1806

0

Высота основания - правильного треугольника - равна или по формуле или по Пифагору h=√(180-45)=√135 = 3√15.
Расстояние от вершины основания до центра (радиус описанной окружности) равно (2/3)*h = 2√15.
Высоту пирамиды - катет треугольника с гипотенузой - боковым ребром и вторым катетом - радиусом описанной около основания окружности найдем по Пифагору: Н=√(16²-(2√15)²) = √(256-60) =14.
Ответ: 14.

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