In an obtuse triangle ABC AB = BC, AB = 15, height CH = 9, find the cos of angle ABC

Since the triangle is isosceles, the angles at the base are equal, which means that the obtuse angle of the triangle is at the vertex B.

Consider a triangle HBC – this is a right-angled triangle: the angle HBC will be external to the angle ABC.

From a right-angled triangle, we express the cosine of the angle, as the ratio of the adjacent leg to the hypotenuse, according to the Pythagorean theorem, we find the adjacent leg:

15 ^ 2 – 9 ^ 2 = 225 – 81 = 144 = 122;

cos ABC = 12/15 = 4/5 = 0.8.

Answer: cos ABC = 0.8