In the triangle ABC AC = BC, AB = 2, the height of AH is equal to √3. find cos A.

Since AН is the height of the ABC triangle, the ABН triangle is rectangular.

In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the leg BН.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 4 – 3 = 1.

BH = 1 cm.

Determine the cosine of the angle AВН.

CosABH = BH / AB = 1/2.

Since, by condition, AC = BC, the triangle ABC is isosceles, and then the angles at the base of AB are equal.

Then CosСAB = CosABH = 1/2.

Answer: The cosine of angle A is 1/2.