In a triangle ABC, c = 90 degrees, AC = 8√3, sine a = 1/8. Find AB.

univerkov | February 23, 2021 | education

Knowing the sine of the angle BAC, we determine the cosine of this angle.

Sin2BAC + Cos2BAC = 1.

Cos2BAC = 1 – Sin2BAC = 1 – (1/7) 2 = (49 – 1) / 49 = 48/49.

CosВАС = √ (48/49) = 4 * √3 / 7.

CosBAC = AC / AB.

AB = AC / CosBAC = 8 * √3 / (4 * √3 / 7) * = 56/4 = 14 cm.

Answer: The length of the AB side is 14 cm.

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