1. **Problem:** Solve for $x$ in a right triangle where one angle is $54^\circ$ and the side adjacent to $x$ is 3. 2. **Formula:** Use the tangent function since we have an angle and the adjacent side, and want the opposite side $x$: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply values:** $$\tan(54^\circ) = \frac{x}{3}$$ 4. **Solve for $x$:** $$x = 3 \times \tan(54^\circ)$$ 5. **Calculate:** $$x = 3 \times 1.37638 = 4.12914$$ 6. **Answer:** $x \approx 4.13$ (rounded to two decimal places) This means the side opposite the $54^\circ$ angle is approximately 4.13 units long.