In triangle ABC, angle C is 90. BC = 12, AC = 4 √7. Find cosB.

First way.

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 112 + 144 = 256.

AB = 16 cm.

Then CosABC = BC / AB = 12/16 = 3/4.

Second way.

Determine the tangent of the angle ABC.

tgАВС = АС / ВС = 4 * √7 / 12 = √7 / 3.

Let’s define the cosine of the angle ABC through the tangent of this angle.

Cos2ABC = 1 / (1 + tg2ABC) = 1 / (1 + 7/9) = 1 / (16/9) = 9/16.

CosABC = 3/4.

Answer: The cosine of angle B is 3/4.