In a right-angled triangle ABC (angle B = 90 degrees) legs AB = 5 and BC = 6. Find cos C.

Let us find the hypotenuse AC of the right-angled triangle ABC according to the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse):

AB² + BC² = AC²;

5² + 6² = AC²;

25 + 36 = AC²;

AC² = 61;

AC = √61.

The cosine of the angle is equal to the ratio of the adjacent leg to the hypotenuse, therefore:

Cos B = BC / AC = 6 / √61.

Answer: 6 / √61