1. **State the problem:** We have a right triangle with legs 10 and $x$, and hypotenuse 13. We need to find the value of $x$ rounded to the nearest tenth. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $a = 10$, $b = x$, and $c = 13$. So, $$10^2 + x^2 = 13^2$$ 4. **Calculate squares:** $$100 + x^2 = 169$$ 5. **Isolate $x^2$:** $$x^2 = 169 - 100 = 69$$ 6. **Solve for $x$:** $$x = \sqrt{69}$$ 7. **Calculate the square root:** $$x \approx 8.3066$$ 8. **Round to the nearest tenth:** $$x \approx 8.3$$ **Final answer:** $x = 8.3$