In a right-angled triangle MKH with a right angle H, the sides are known: MK = 25, MH = 20, KH = 15.

In a right-angled triangle MKH with a right angle H, the sides are known: MK = 25, MH = 20, KH = 15. Find the cosine of the angle M.

In order to solve this problem, you need to carefully study the condition and draw a picture to facilitate understanding of the situation. By condition, three sides are given. We can apply the cosine theorem to find the angle we want.

KH ^ 2 = MK ^ 2 + MH ^ 2 – 2 * MKKH cosM.

cosM = (15 ^ 2 – 25 ^ 2 – 20 ^ 2) / (2 * 25 * 20) = (225 – 625 – 400) / 1000 = -800 / 1000 = -4 / 5 = -0.8.

Therefore, our answer is -0.8.