1. **State the problem:** We need to solve for $x$ in the equation $\sin 35^\circ = \frac{5}{x}$ and round the answer to the nearest tenth. 2. **Recall the sine definition:** In a right triangle, $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$. 3. **Set up the equation:** Given $\sin 35^\circ = \frac{5}{x}$, where 5 is the length of the side opposite the 35-degree angle and $x$ is the hypotenuse. 4. **Solve for $x$:** Multiply both sides by $x$ to get $$x \sin 35^\circ = 5$$ Then divide both sides by $\sin 35^\circ$: $$x = \frac{5}{\sin 35^\circ}$$ 5. **Calculate $\sin 35^\circ$:** Using a calculator, $$\sin 35^\circ \approx 0.574$$ 6. **Substitute and compute:** $$x = \frac{5}{0.574}$$ 7. **Simplify with cancellation:** $$x = \frac{5}{\cancel{0.574}} \approx 8.71$$ 8. **Round to the nearest tenth:** $$x \approx 8.7$$ **Final answer:** $x = 8.7$ which corresponds to option C.