1. **State the problem:** We need to solve for $x$ in a right triangle $\triangle TYW$ where $\angle T$ is $90^\circ$, side $YT = x$, side $YW = 95$, and $\angle W = 31^\circ$. 2. **Identify the sides relative to $\angle W$:** - $YT = x$ is the side opposite $\angle W$. - $YW = 95$ is the hypotenuse. 3. **Use the sine function:** The sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\sin(31^\circ) = \frac{x}{95}$$ 5. **Solve for $x$:** Multiply both sides by 95: $$x = 95 \times \sin(31^\circ)$$ 6. **Calculate $\sin(31^\circ)$:** $$\sin(31^\circ) \approx 0.5150$$ 7. **Find $x$:** $$x = 95 \times 0.5150 = 48.925$$ 8. **Round to the nearest tenth:** $$x \approx 48.9$$ **Final answer:** $x \approx 48.9$