In triangle ABC, angle C = 90 °, CH – height AC = 10, AH = √91. Find the cosine cos B.

Consider a right-angled triangle ACH, in which the CH height is an unknown leg. Let’s use the Pythagorean theorem and find CH:
CH = √ (AC² – AH²) = √ (100 – 91) = √9 = 3.
In the ASN triangle, we write down the sine of angle A, which in turn is equal to the cosine of angle B, which must be found by condition.
Cos B = sin A = CH / AC = 3/10 = 0.3.
Answer: The cosine of angle B is 0.3.