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 in the triangle:

1 side = 10;
2 side = 9;
сos of the angle between them = 4/5.
Solution:

The area of a triangle is half the product of the sides and the sine of the angle between them.

We get:

S = 1/2 * 10 * 9 * sin a = (10 * 9) / 2 * √ (1 – cos ^ 2 a) = 10/2 * 9 * √ (1 – (4/5) ^ 2) = 5 * 9 * √ (1 – 0.8 ^ 2) = 45 * √ (1 – 0.64) = 45 * √0.36 = 45 * 0.6 = 45 * 6/10 = 45 * 3/5 = 45/5 * 3 = 9 * 3 = 27;

This means that the area of the triangle is 27.

Answer: S = 27.