In triangle ABC, angle C is 90 degrees, CH is height, AC = 4, sinA = √7 / 4. Find AH.

univerkov | July 29, 2021 | education

Determine the cosine of the angle BAC.

Sin2BAC + Cos2BAC = 1.

Cos2BAC = 1 – Sin2BAC = 1 – 7/16 = (16 – 7) / 16 = 9/16.

CosBAC = 3/4.

Then CosBAC = AH / AC.

AH = AC * CosBAC = 4 * √7 / 4 = √7 cm.

Answer: The length of the segment AH is equal to √7 cm.

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