1. **State the problem:** We need to find the length of side $x$ (SU) in right triangle SUT where angle $S = 72^\circ$, side $TU = 9.4$, and angle $T$ is the right angle. 2. **Identify the sides relative to angle $S$:** - Side $TU = 9.4$ is opposite angle $S$. - Side $SU = x$ is the hypotenuse. 3. **Use the sine function:** The sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Set up the equation:** $$\sin(72^\circ) = \frac{9.4}{x}$$ 5. **Solve for $x$:** Multiply both sides by $x$: $$x \sin(72^\circ) = 9.4$$ Divide both sides by $\sin(72^\circ)$: $$x = \frac{9.4}{\sin(72^\circ)}$$ 6. **Calculate $\sin(72^\circ)$:** $$\sin(72^\circ) \approx 0.9511$$ 7. **Substitute and compute:** $$x = \frac{9.4}{0.9511} \approx 9.88$$ 8. **Round to the nearest tenth:** $$x \approx 9.9$$ **Final answer:** $$\boxed{9.9}$$