In triangle ABC, angle C is 90, CH-height, AC = 20, AH = 16. Find cosB.

Since CH is the height, the triangle CHA is rectangular, then by determining the sine of the angle we get:

sin (A) = CH / AC = 16/20 = 4/5.

Triangle ABC is rectangular by the problem statement, then the equality is true:

cos ^ 2 (B) + sin ^ 2 (A) = 1;

cos ^ 2 (B) = 1 – sin ^ 2 (A) = 1 – 16/25 = 9/25;

cos (B) = 3/5.

Answer: the required cosine of angle B is 3/5.