In triangle ABC, angle C is 90 degrees, sin A = 24/29, AC = √265. Find AB.

univerkov | September 24, 2021 | education

In a right-angled triangle ABC, we define the cosine of the angle BAC.

Sin2BAC + Cos2BAC = 1.

Cos2BAC = 1 – Sin2BAC = 1 – 576/841 = 265/841.

CosBAC = √265 / 29.

Then: CosBAC = AC / AB.

AB = AC / CosBAC = √265 / (√265 / 29) = 29 cm.

Answer: The length of the AB side is 29 cm.

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