In an acute-angled triangle ABC, the height AH is 203√ and the side AB is 40. Find cosB.

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 40, leg AH = 20√3. We find the ВН leg according to the Pythagorean theorem:

40² – (20√3) ² = BH².

BH² = 1600 – 1200 = 400.

BH = 20.

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

ВН \ AB = 20 \ 40 = 0.5.

So our answer is 0.5.