Предмет: Геометрия, автор: Olezhka11

В прямоугольнике ABCD диагонали пересекаются в точке O найти периметр треугольника AOB, если угол CAD=30°, AC=14см

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Автор ответа: Крот2002

Т.к. диагонали прямоугольника в точке пересечения делятся пополам, то АО = АС : 2 = 14 : 2 = 7 см. Т.к. ВО = АО, то ВО = 7. Т.к. В прямоугольнике все углы = 90°, то угол ВСО = угол ВАD - угол САD = 90° - 30° = 60°. Т.к. сумма углов треугольника равна 180°, то треугольник АОВ - равносторонний => АВ = ВО = АО = 7 см => Р= 7*3 = 21 см

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