In triangle ABC, AB = BC, and the height AH divides side BC into segments BH = 12 and CH = 3. Find cosB.

Given: triangle ABC;

AB = BC;

AH – height;

BH = 12;

CH = 3;

Find: cosB -?.

Because by the condition AB = BC, then the triangle ABC is isosceles.

AB = BC = BH + CH = 12 + 3 = 15.

Consider a triangle ABH. It is rectangular, with a right angle AHB, because AH is the height. For a right-angled triangle, the aspect ratios apply. So the cosine of an angle is the ratio of the leg adjacent to this angle to the hypotenuse of the triangle, i.e .:

cosB = BH / AB = 12/15 = 0.8.

Answer: cosB = 0.8.