1. **State the problem:** We have a right triangle with an angle of 63° and the side opposite this angle is 16. We need to find the hypotenuse $x$. 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, $\theta = 63^\circ$, opposite side = 16, and hypotenuse = $x$. So, $$\sin(63^\circ) = \frac{16}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\sin(63^\circ)$: $$x \times \sin(63^\circ) = 16$$ $$\cancel{x} = \frac{16}{\sin(63^\circ)}$$ 5. **Calculate the value:** Using a calculator, $$\sin(63^\circ) \approx 0.8910$$ $$x = \frac{16}{0.8910} \approx 17.96$$ 6. **Final answer:** The hypotenuse $x$ is approximately 17.96 units.