In the ABC triangle, the angle is C = 90, tgA = 8/15, BC = 4. Find AB.

Given a right-angled triangle ABC, angle C is 90 °, tan A = 8/15, BC = 4 cm. Find AB.

In a right-angled triangle, the tangent of an acute angle is equal to the ratio of the opposite leg to the adjacent leg, i.e.

tg A = BC / AC,

4 / AC = 8/15,

AC = (4 * 15) / 8 = 15/2.

By the Pythagorean theorem, we find the hypotenuse of the triangle:

AB ^ 2 = (15/2) ^ 2 + 4 ^ 2 = 225/4 + 16/1 = 289/4,

AB = 17/2.

Answer: 17/2.