1. **State the problem:** We need to find the length of the hypotenuse $x$ in a right triangle where the legs are 15 and 11. 2. **Formula used:** According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse $x$ is equal to the sum of the squares of the other two sides: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs of the triangle. 3. **Apply the formula:** Substitute $a = 15$ and $b = 11$: $$x^2 = 15^2 + 11^2$$ 4. **Calculate squares:** $$x^2 = 225 + 121$$ $$x^2 = 346$$ 5. **Find $x$ by taking the square root:** $$x = \sqrt{346}$$ 6. **Calculate the square root and round to the nearest tenth:** $$x \approx 18.6$$ **Final answer:** The length of the hypotenuse $x$ is approximately **18.6**.