1. **State the problem:** We need to find the angle $x$ in a right triangle $UTS$ where the right angle is at $T$. 2. **Given:** Side $TS = 4.3$, hypotenuse $US = 9.8$, and angle $x$ is at vertex $U$. 3. **Formula:** Use the sine function since sine relates the opposite side to the hypotenuse: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Identify opposite side:** The side opposite angle $x$ is $TS = 4.3$. 5. **Set up the equation:** $$\sin(x) = \frac{4.3}{9.8}$$ 6. **Calculate the ratio:** $$\sin(x) = 0.4387755$$ 7. **Find angle $x$ by taking inverse sine:** $$x = \sin^{-1}(0.4387755)$$ 8. **Calculate $x$:** $$x \approx 26.1^\circ$$ 9. **Answer:** The angle $x$ is approximately $26.1^\circ$ when rounded to the nearest tenth of a degree.