In the ABC triangle it is known that AC = BC = 16 and cos A = 0.75 find AB.

Triangle ABC is isosceles with base AB. The height CH, lowered from point C to the base AB, divides it in half:

AH = AB / 2.

The AСН triangle is rectangular. The ratio of the segment AH to the AC side is equal to the cosine of the angle A:

AH / AC = cos (A);

AB / (2 * AC) = 0.75;

AB = 1.5 * AC = 1.5 * 16 = 24.

Answer: AB = 24.