In an acute-angled triangle ABC, the height AH is 9 √39 and the side of AB is 60. Find cos B

1. First you need to remember the formula for the cos angle, in our case the formula will look like this: cos B = BH / AB;

2. We do not know BH, so we need to find it by the Pythagorean theorem:
BH ^ 2 = AB ^ 2 – AH ^ 2;
BH ^ 2 = 60 ^ 2 – (9√39) ^ 2;
BH ^ 2 = 3600 – 81 * 39;
BH ^ 2 = 3600-3159;
BH ^ 2 = √441;
BH = 21.

3. Now we find cos, substituting the values into the formula:
cos B = 21/60;
cos B = 0.35.

Answer: cos B = 0.35