In triangle ABC, angle C is 90º, AB = 25, cosB = 4/5 find AC.

Since the cosine of the angle is the ratio of the adjacent side to the hypotenuse, in our case, cos B = CB / AB = 4/5.

Let’s make the proportion, since we know the AB side: CB / AB = 4/5.

Let’s use the method of proportion, or “crosswise”: 5 CB = 4 AB.

Let’s find CB: CB = 4 * AB / 5 = 4 * 25/5 = 4 * 5 = 20. So CB = 20.

Now let’s use the Pythagorean theorem: AC ^ 2 = AB ^ 2 + BC ^ 2.

Substitute the numbers we know: AC ^ 2 = 20 * 20 + 25 * 25 = 400 + 625 = 1025.

Find AC: 1025 ^ 1/2 = 5 roots with 41.

Answer: 5 roots from 41.