In a right-angled triangle ABC, angle C = 90 °, find the value of the sine of angle A if the cosine of angle B is 3/5.

Given: right-angled triangle ABC;

angle C = 90;

cos B = 3/5;

Find: sin A -?

Solution:

Consider a right-angled triangle ABC. The cosine of angle B is equal to the ratio of the adjacent leg to the hypotenuse. The hypotenuse is the AB side, the adjacent leg is the BC side. Hence:

cos B = BC / AB.

The sine of angle A is equal to the ratio of the opposite leg to the hypotenuse. The opposite leg is the BC side. Hence:

sin A = BC / AB = cos B = 3/5.

Answer: 3/5.