In triangle ABC, angle C is 90, AB = 5, cosine of angle B is 3/5. find the AC.

First way.

Through the hypotenuse AB and and the cosine of the angle ABC, we determine the length of the leg BC.

CosABC = BC / AB.

BC = AB * CosABC = 5 * (3/5) = 3 cm.

By the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16.

AC = 4 cm.

Second way.

Determine the sine of the angle ABC.

Sin2ABS = 1 – Cos2ABS = 1 – 9/25 = 16/25.

SinABS = 4/5.

SinABC = AC / AB.

AC = AB * SinABC = 5 * 4/5 = 4 cm.

Answer: The length of the speaker side is 4 cm.