# In triangle ABC, angle C is 90, АС = 15, cosB = √7 / 4. Find AB

October 9, 2021 | education

| Determine the sine of the angle ABC.

Sin2ABC = 1 – Cos2ABC = 1 – (√7 / 4) 2 = 1 – 7/16 = 9/16

SinABS = 3/4.

Through the leg AC and the sine of the corner opposite to it, we determine the length of the hypotenuse AB.

SinABC = AC / AB.

AB = AC / SinABC = 15 / (3/4) = 15 * 4/3 = 20 cm.

Answer: The length of the AB side is 20 cm.