Предмет: Геометрия, автор: kotsem11

две стороны треугольника равны 2 см и 17 см образуют острый угол , тангенс которого равен 8/15 .найдите длину 3 стороны треугольника ?

Ответы

Автор ответа: awkut

Переведем tg в cos используя соотношение
1 + tg^2 a = 1/cos^2 a
1+(8/15)^2 = 1/cos^2 a
cosa =15/корень(64+225) = 15/17
по формуле определения стороны треугольника через 2 стороны и угол между ними
x = корень(2^2 + 17^2 - 2*2*17*cosa) = корень(4 + 289 - 60) = 15,3
Ответ приближенный результат - 15,3 см

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