We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Let's denote the length of the other leg by x. Then we have:
x^2 + 17^2 = 24^2
Simplifying and solving for x, we get:
x^2 + 289 = 576
x^2 = 287
x ≈ 16.91
Therefore, the length of the other leg of the right triangle is approximately 16.91 feet.