Sides of a triangle = 4.5.6. Find the cosine of the angle opposite the larger side.

Let the sides of the triangle a = 4; h = 5; c = 6.

Find cos (<C), Use the cosine theorem for a given triangle and angle <C:

c ^ 2 = a ^ 2 + b ^ 2 – 2 * b * c * cos (<C); substitute all the values in this formula, and then express the unknown – cos (<C).

6 ^ 2 = 4 ^ 2 + 5 ^ 2 – 2 * 4 * 5 * cos (<C); 36 = 16 + 25 – 40 * cos (<C);

40 * cos (<C) = 5; cos (<C) = 5/40 = 1/8.