In a triangle, one of the sides is 10, the other is 9, and the cosine of the angle between them is 4/5.

In a triangle, one of the sides is 10, the other is 9, and the cosine of the angle between them is 4/5. Find the area of the triangle

It is known that cos2α + sin2α = 1. Hence, sin2α = 1 – cos2α. We can find the sine of the angle between the given sides:

sin2α = 1 – (4/5) ^ 2 = 1 – 16/25 = 9/25;

sinα = √ (9/25) = 3/5.

The area of a triangle can be defined as half of the product of the lengths of two adjacent sides by the sine of the angle between them:

S = 0.5 * 10 * 9 * 3/5 = 27.