In a right-angled triangle ABC leg BC is 15 cm, sin B = 0.8 Find leg AC.

univerkov | May 28, 2021 | education

Determine the cosine of the angle ABC.

Cos2ABC = 1 – Sin2BC = 1 – 0.64 = 0.36.

CosABC = 0.6.

Then AB = BC / CosABC = 15 / 0.6 = 25 cm.

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

AC ^ 2 = AB ^ 2 – BC ^ 2 = 625 – 225 = 400.

AC = 20 cm.

Answer: The length of the AC leg is 20 cm.

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