1. **State the problem:** We have a right triangle with one leg of length 9, an angle of 45° opposite the side labeled $x$, and we need to find the value of $x$ in simplest form. 2. **Recall the relevant formula:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** Here, $\theta = 45^\circ$, opposite side is $x$, adjacent side is 9, so: $$\tan(45^\circ) = \frac{x}{9}$$ 4. **Evaluate $\tan(45^\circ)$:** We know $\tan(45^\circ) = 1$, so: $$1 = \frac{x}{9}$$ 5. **Solve for $x$:** Multiply both sides by 9: $$9 \times 1 = x$$ $$x = 9$$ 6. **Final answer:** The value of $x$ is 9.