In triangle ABC, angle C is 90 degrees, tg A = 7/24. Find cos B.

In a right-angled triangle, the tangent of the angle is equal to the ratio of the opposite leg to the adjacent one, that is

tg A = BC / AC.

That is, the side BC is a multiple of 7, and the side AC is 24. Take the simplest case, let BC = 7, and AC = 24. Then, by the Pythagorean theorem, you can find the hypotenuse AB:

AB = √ (BC² + AC²) = √ (7² + 24²) = √ (49 + 576) = √625 = 25.

The cosine of the angle in a right-angled triangle is equal to the ratio of the leg adjacent to the angle to the hypotenuse. That is, to find cos B, you need to divide BC by AB. Let us find this ratio and, at the same time, the cosine of the angle B:

cos B = 7/25 = 0.28.

Answer: cos B = 0.28.