In triangle ABC, angle C is 90 degrees. CH – height, AB = 49 cos A 6/7 Find AH

By the definition of cosine, we have:
AC = AB * cosA
AC = 479 * 6/7 = 42
According to metric ratios in a right-angled triangle (the square of the leg is equal to the product of the hypotenuse and the projection of this leg to the hypotenuse) AH is the projection of the leg AC:
AC ^ 2 = AH * AB
AH = AC ^ 2 / AB
AH = 42 ^ 2/49 = 36