1. **State the problem:** We have a right triangle with legs of length 8 and $x$, and hypotenuse of length 17. We need to find the exact value of $x$. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $a=8$, $b=x$, and $c=17$. So, $$8^2 + x^2 = 17^2$$ 4. **Calculate squares:** $$64 + x^2 = 289$$ 5. **Isolate $x^2$:** $$x^2 = 289 - 64$$ $$x^2 = 225$$ 6. **Take the square root:** $$x = \pm \sqrt{225}$$ $$x = \pm 15$$ Since length cannot be negative, we take: $$x = 15$$ 7. **Check if the side lengths form a Pythagorean triple:** The triple is $(8, 15, 17)$, which is a well-known Pythagorean triple. **Final answer:** $$x = 15$$ **Yes, the side lengths form a Pythagorean triple.**