The sides of the triangle are 7, 3, and 8. Find the cosine of the larger angle of the triangle.

In a triangle, opposite the larger side, there is a larger angle, opposite the smaller side, a smaller angle.

In a triangle with sides a = 7, b = 3, c = 8, side c will be larger. The angle between sides a and b will be a large angle ϒ.

By the cosine theorem: In a triangle, the square of any side is equal to the sum of the squares of the other two sides without the double product of these sides by the cosine of the angle between them.

c ^ 2 = a ^ 2 + b ^ 2 – 2ab * cos ϒ – express cos ϒ;

2ab cos ϒ = a ^ 2 + b ^ 2 – c ^ 2;

cos ϒ = (a ^ 2 + b ^ 2 – c ^ 2) / (2ab);

cos ϒ = (7 ^ 2 + 3 ^ 2 – 8 ^ 2) / (2 * 7 * 3) = (49 + 36 – 64) / 42 = 21/42 = 1/2 = 0.5.

Answer. 0.5.