1. **State the problem:** We have a right triangle with a right angle at vertex T, hypotenuse 95, angle at W is 31°, and side opposite angle W is $x$. 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 side opposite the angle to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 31^\circ$, opposite side = $x$, hypotenuse = 95. $$\sin(31^\circ) = \frac{x}{95}$$ 4. **Solve for $x$:** Multiply both sides by 95: $$x = 95 \times \sin(31^\circ)$$ 5. **Calculate $\sin(31^\circ)$:** $$\sin(31^\circ) \approx 0.5150$$ 6. **Find $x$:** $$x = 95 \times 0.5150 = 48.925$$ 7. **Round to nearest tenth:** $$x \approx 48.9$$ **Final answer:** $$x = 48.9$$