What is the length of one leg of the triangle

Use the Pythagorean theorem for right triangles to solve this

a^2 + b^2 = c^2 where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse

so:

8^2 + b^2 = 17^2 solve for the second leg, b

64 + b^2 = 289

b^2 = 289 - 64 = 225

b = 15