# In triangle ABC, angle C is 90, AC is 15, cosine of angle B is √7 / 4. Find AB

September 12, 2021 | education

| Knowing the cosine of the angle ABC, we determine the sine of this angle.

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

SinABC = 3/4.

Through the sine of the angle and the opposite leg, we determine the length of the hypotenuse AB.

SinABS = AC / AB.

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

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

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