Question

В остроугольном треугольнике abc высота ah равна 27 корней из 3, а сторона ab равно 54. Найдите cosB

Answer 1

Из условия вытекает sin B = (27√3) / 54 = √3 / 2.
Косинус В = √(1-sin²B) = √(1-(3/4)) = √(1/4) = 1/2/
Можно было и по другому решить:
синусу √3 / 2 соответствует угол 60°, а косинус 60° = 1/2.

Answer 2

Для решения этой задачи нам необходимо найти значение угла B. Мы знаем, что высота треугольника равна 27√3, а сторона ab равна 54.

Используя формулу для высоты треугольника, мы можем найти значение стороны ac: ah = (ac * sinB) / 2 27√3 = (ac * sinB) / 2 ac * sinB = 54√3 ac = 54√3 / sinB

Так как сторона ab равна 54, мы можем найти значение стороны bc: bc = 2 * ab * sinB bc = 2 * 54 * sinB bc = 108 * sinB

Теперь мы можем использовать теорему Пифагора, чтобы найти значение стороны ac: ac^2 + bc^2 = ab^2 (ac)^2 + (108 * sinB)^2 = 54^2 (ac)^2 + 11664 * (sinB)^2 = 2916 (ac)^2 = 2916 - 11664 * (sinB)^2 (ac)^2 = 2916 - 11664 * (1 - (cosB)^2) (ac)^2 = 2916 - 11664 + 11664 * (cosB)^2 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 = 11664 * (cosB)^2 - 8748 (ac)^2 =