In a right-angled triangle ABC, the hypotenuse is AB = 17, AC = 15. Find the tangent of angle B.

To calculate, we need to know the length of the side BC. for this we use the Pythagorean theorem. Since AB is a hypotenuse, BC can be found using the following formula:

BC = √ (AB² – AC²).

Let’s find the side we need:

BC = √ (17² – 15²) = √ (289 – 225) = √64 = 8.

The tangent of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the adjacent leg. Hence, the tangent of angle B is

tg B = AC / BC.

Find the required tangent:

tg B = 15/8 = 1.875.

Answer: The tangent of angle B in right-angled triangle ABC is 1.875.