In an acute-angled triangle, the height AH is 19√21, the side AB = 95. Find cos B.

In order to solve this problem, you need to draw a picture or imagine it in your mind.

АН – height, which means triangle ABН – rectangular. Its hypotenuse AB is equal to 95, leg AH = 19√21. We find the ВН leg according to the Pythagorean theorem:

95² – (19√21) ² = BH².

BH² = 9025 – 7581 = 1444.

BH = 38.

Cosine is the ratio of the adjacent leg to the hypotenuse, in our case:

ВН / AB = 38/95 = 0.4.

Therefore our answer is 0.4.