In a right-angled triangle ABC, the angle is C = 90 °. Find the leg length AC if the angle is B = 45 ° and leg BC = 21.

First way.

The sum of the inner angles of the triangle is 180, then the angle BAC = 180 – 90 – 45 = 45.

Since the angles at the base of AB are equal, the triangle ABC is rectangular and isosceles, and therefore AC = BC = 21 cm.

Second way.

The tangent of a rectangular angle is the ratio of the opposite leg to the adjacent one.

tgABC = AC / BC.

AC = BC * tg45 = 21 * 1 = 21 cm.

Answer: The length of the AC leg is 21 cm.