Предмет: Геометрия, автор: dencheck

Один из углов прямоугольного треугольника = 60градусов, а сумма гипотинузы и меньшего катета равна 42 см, найдите гипатинузу?

Ответы

Автор ответа: Орхидей
0
Так как треугольник прямоугольный,то 1-ый угол= 60 градусов(по условию), 2-ый угол=90 градусам( по условию). Найдем 3-ый угол.
Сумма всех углов треугольника равна 180 градусам. Значит, 3-ый угол равен 180-(90+60)=30 градусам. 
Катет,лежащий против угла в 30 градусов равен половине гипотенузы. Значит, гипотенуза равна 28.( Проверить можно по теореме Пифагора).
Автор ответа: eden01
0
Пусть гипотенуза=х, тогда меньший катет=42-х.
(т.к. их сумма 42. Проверим: х+(42-х)=42, х+42-х=42, 42=42)
Третий угол треугольника =90-60=30градусов. Катет, лежащий против угла 30 градусов, равен половине гипотенузы:
42-х=1/2 * х
3х/2=42
3х=84
х=28(см) - гипотенуза.
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