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Консультация № 146014
04.10.2008, 22:01
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здравствуйте,уважаемые эксперты.помогите пожалуйста решить задачу по геометрии
. Сторона ромба образует с его диагоналями углы, разность которых равна 44°. Определить углы ромба.
. Сторона ромба образует с его диагоналями углы, разность которых равна 44°. Определить углы ромба.
Обсуждение
Неизвестный
06.10.2008, 16:56
общий
это ответ
Здравствуйте, G-buck!
Рассмотрим треугольник образованный половинками диагоналей и стороной ромба. Он прямоугольный, сумма углов при гипотенузе(стороне ромба) равна 90°(180°-90°=90°), значит меньший угол равен (90°-44°)/2=23°;
а больший 23°+44°=67°.
Эти углы являются половинами углов ромба, т.к. все 4 треугольника, образованные диагоналями ромба, равны.
Ответ: меньший угол ромба равен 23°*2=46°, больший угол равен 67°*2=134°.
Приложение:
Диагонали ромба пересекаются под прямым углом.
Рассмотрим треугольник образованный половинками диагоналей и стороной ромба. Он прямоугольный, сумма углов при гипотенузе(стороне ромба) равна 90°(180°-90°=90°), значит меньший угол равен (90°-44°)/2=23°;
а больший 23°+44°=67°.
Эти углы являются половинами углов ромба, т.к. все 4 треугольника, образованные диагоналями ромба, равны.
Ответ: меньший угол ромба равен 23°*2=46°, больший угол равен 67°*2=134°.
Приложение:
Диагонали ромба пересекаются под прямым углом.
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