In triangle ABC, angle C is 90◦, BC = 10, cosA = 0.6 Find the height CH.

The height CH of the right-angled triangle ABC divides it into two right-angled triangles similar to the triangle ABC. In a triangle BCH, the angle BCH is equal to the angle A of the original triangle. Hence cos BCH = cos A = 0.6. In the triangle BCH, CH is the adjacent leg, and BC is the hypotenuse, thus:

CH = BC * cos BCH = 10 * 0.6 = 6.