1. **State the problem:** We have a right triangle with legs of lengths 9 and 15, and we need to find the length of the hypotenuse. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Apply the formula:** Substitute $a=9$ and $b=15$: $$c^2 = 9^2 + 15^2$$ 4. **Calculate squares:** $$c^2 = 81 + 225$$ 5. **Sum the squares:** $$c^2 = 306$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{306}$$ 7. **Approximate the square root:** $$c \approx 17.4929$$ 8. **Round to the nearest tenth:** $$c \approx 17.5$$ **Final answer:** The length of the hypotenuse is approximately $17.5$.