The two sides of the triangle are 17 and 8, and the cosine of the angle between them is 15/17.

The two sides of the triangle are 17 and 8, and the cosine of the angle between them is 15/17. Find the area of this triangle.

It is known that cos2α + sin2α = 1. Knowing that cos α = 15/17, we can find sin α:

sin2α = 1 – cos2α = 1 – (15/17) ^ 2 = 1 – (225/289) = (289 – 225) / 289 = 64/289;

sinα = 8/17.

The area of a triangle is equal to half the product of the lengths of two sides by the sine of the angle between them:

S = 0.5 * a * b * sinα = 0.5 * 17 * 8 * 8/17 = 32.