1. **State the problem:** We have a right triangle with a hypotenuse of length 10, an angle of 31°, and the side opposite this angle labeled as $x$. We need to find $x$. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 31^\circ$, opposite side = $x$, hypotenuse = 10. $$\sin(31^\circ) = \frac{x}{10}$$ 4. **Solve for $x$:** Multiply both sides by 10: $$x = 10 \times \sin(31^\circ)$$ 5. **Calculate $\sin(31^\circ)$:** Using a calculator, $$\sin(31^\circ) \approx 0.5150$$ 6. **Find $x$:** $$x = 10 \times 0.5150 = 5.15$$ 7. **Round to the nearest tenth:** $$x \approx 5.2$$ **Final answer:** $x = 5.2$ (rounded to the nearest tenth).