In triangle ABC, angle C = 90 degrees, AB = 2, BC = √ 3. find cosA

univerkov | February 27, 2021 | education

First way.

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

SinBAC = BC / AB = √3 / 2.

Determine the cosine of the angle BAC.

Cos2BAC + Sin2BAC = 1.

Cos2BAC = 1 – Sin2BAC = 1 – (3/4) = 1/4.

CosBAC = 1/2.

Second way.

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

AC ^ 2 = AB ^ 2 – BC ^ 2 = 4 – 3 = 1.

AC = 1 cm.

Then CosBAC = AC / AB = 1/2.

Answer: The cosine of the angle BAC is 1/2.

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