Final answer:
Using the Pythagorean Theorem, we find that the length of the third side of the right triangle is 8 units.
Step-by-step explanation:
To find the length of the third side of a right triangle when the lengths of the hypotenuse and another side are given, we can use the Pythagorean Theorem. According to the theorem (a2 + b2 = c2), the sum of the squares of the two legs a and b equals the square of the hypotenuse c. In this case, the hypotenuse c is 17 and one of the legs a is 15.
We can calculate the length of the other leg b by rearranging the theorem to solve for b: b2 = c2 - a2. Then, b2 = 172 - 152, which calculates to b2 = 289 - 225. So b2 = 64 and b = √64, which means b = 8. Therefore, the length of the third side is 8 units.