1. **State the problem:** We have a right triangle with one angle of 45°, the hypotenuse is 9, and the side opposite the 45° angle is labeled $x$. We need to find $x$. 2. **Recall the formula:** 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:** For $\theta = 45^\circ$: $$\sin(45^\circ) = \frac{x}{9}$$ 4. **Use the known value:** $$\sin(45^\circ) = \frac{\sqrt{2}}{2}$$ 5. **Set up the equation:** $$\frac{\sqrt{2}}{2} = \frac{x}{9}$$ 6. **Solve for $x$:** Multiply both sides by 9: $$x = 9 \times \frac{\sqrt{2}}{2}$$ 7. **Simplify:** $$x = \frac{9\sqrt{2}}{2}$$ **Final answer:** $$x = \frac{9\sqrt{2}}{2}$$