Предмет: Алгебра, автор: Groomхахаха

Помогите решить.

В прямоугольном треугольнике гипотенуза равна 92 , а один из острых углов равен 45 °. Найдите площадь треугольника.

Ответы

Автор ответа: danil13221
1
Допустим это будет ΔАВС, где АВ - гипотенуза, а АС и ВС - катеты, угол С = 90
Угол В = 45, значит, что и угол А = 45Из этого следует, что ΔАВС - равнобедренныйПо теореме Пифагора получается:АВ²= АС²+ВС²Пусть АС=х, тогда и ВС=х, так как ΔАВС - равнобедренный
АВ²=х²+х²=2х²4900=2х²2450=х²х=√2450
S = 0.5*АС*ВС= 0.5*√2450*√2450= 0.5*2450=1225
Ответ: 1225


Groomхахаха: Большое спасибо за решение! ;)
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