In the triangle ABC AC = BC, AB = 25, the height of AH is 15. Find cos A

The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. This means that the cosine of the angle A is equal to the ratio of the adjacent leg AH to the hypotenuse AC.

cos A = AH / AC.

In an isosceles triangle, the height drawn to the base is also both the bisector and the median. Means:

AH = HB = 25/2 = 12.5.

Let’s find the AS according to the Pythagorean theorem:

AC² = CH² + AH²;

AC² = 15² + 12.5²;

AC² = 225 + 156.25;

AC² = 381.25;

AC = √381.25;

cos A = 12.5 / √381.25 = 12.5 / 19 √ 20.25.