1. **Problem statement:** We have a right triangle with a hypotenuse of length 15, an angle of 51°, and the side opposite this angle labeled as $x$. We need to find the length of side $x$. 2. **Formula used:** In a right triangle, the side opposite an angle is related to the hypotenuse by the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 51^\circ$, opposite side = $x$, hypotenuse = 15, so: $$\sin(51^\circ) = \frac{x}{15}$$ 4. **Solve for $x$:** Multiply both sides by 15: $$x = 15 \times \sin(51^\circ)$$ 5. **Calculate $\sin(51^\circ)$:** Using a calculator or sine table, $$\sin(51^\circ) \approx 0.7771$$ 6. **Find $x$:** $$x = 15 \times 0.7771 = 11.6565$$ 7. **Final answer:** The missing side $x$ is approximately $$\boxed{11.66}$$