1. **State the problem:** We are given a right triangle with legs of lengths 5 inches and 9 inches, and we need to find the hypotenuse $h$. 2. **Formula used:** For a right triangle, the Pythagorean theorem states: $$h^2 = a^2 + b^2$$ where $a$ and $b$ are the legs, and $h$ is the hypotenuse. 3. **Apply the formula:** $$h^2 = 5^2 + 9^2$$ $$h^2 = 25 + 81$$ $$h^2 = 106$$ 4. **Solve for $h$:** $$h = \sqrt{106}$$ 5. **Simplify the square root if possible:** 106 is not a perfect square and cannot be simplified further. 6. **Final answer:** $$h = \sqrt{106} \approx 10.295$$ inches. This means the hypotenuse of the triangle is approximately 10.295 inches.