In an isosceles triangle ABC with base AC, the lateral side AB = 16, and the height

In an isosceles triangle ABC with base AC, the lateral side AB = 16, and the height drawn to the base is 8 out of three roots. find the cosine of the angle A.

Since triangle ABC is isosceles, its height BH is also the median of the triangle, and therefore AH = CH = AC / 2 = 16/2 = 8 cm.

In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 64 + 192 = 256.

AB = 16 cm.

Then the cosine of the angle BAH is equal to the ratio of the adjacent leg AH to the hypotenuse AB.

CosBAH = 8/16 = 1/2.

Answer: CosВАH = 1/2.