In the triangle ABC AC = BC, AB = 12, AH – height, BH = 6. Find the cosine of the angle BAC

In the triangle ABC AC = BC, AB = 12, AH – height, BH = 6. Find the cosine of the angle BAC You need to find the cosine of the angle BAC, not the cosine HAB

Triangle ABC is isosceles, based on the conditions of the problem, namely from the equality of its sides AC and BC.

Therefore, the angles of the triangle BAC and CBA are equal, according to the theorem of angles at the base of an isosceles triangle.

Let us determine the cosine of the angle CBA, knowing by the condition of the problem that the length BH is 6 centimeters, and the length of the base of the triangle AB is 12 centimeters, and also that the cosine is the ratio of the adjacent leg to the hypotenuse:

cos CBA = 6/12 = 1/2.

Answer: cos BAC equals 1/2.