Предмет: Геометрия, автор: Frolova1998

площадь прямоугольного треугольника равна корень из 3/2 . Один из острых углов равен 30 градусам . Найдите длину гипотенузы

Ответы

Автор ответа: 09876431235724982

tg30°=b/a
Отсюда a=b/tg30°
Формула площади прямоугольного треугольника
S=ab/2
Подставляя, получаем
S=b·b/(2tg30°)=b²/(2tg30°)
b²=2S·tg30°
b²=2*√3/2*1/√3=1
b=1
Гипотенуза в два раза больше угла, лежащего напротив угла 30°
c=2b=2
Ответ: 2

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