1. **State the problem:** We need to find the length of side $x$ (WU) in right triangle WUV, where the right angle is at $V$, side $WV = 9.2$, and angle $U = 50^\circ$. 2. **Identify the sides relative to angle $U$:** - Side $WV = 9.2$ is adjacent to angle $U$. - Side $WU = x$ is the hypotenuse. 3. **Use the cosine function:** The cosine of an angle in a right triangle is the ratio of the adjacent side over the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 4. **Set up the equation:** $$\cos(50^\circ) = \frac{9.2}{x}$$ 5. **Solve for $x$:** $$x = \frac{9.2}{\cos(50^\circ)}$$ 6. **Calculate the value:** $$\cos(50^\circ) \approx 0.6428$$ $$x = \frac{9.2}{0.6428} \approx 14.3$$ 7. **Final answer:** The length of side $WU$ is approximately $14.3$ (rounded to the nearest tenth).