1. **State the problem:** We have a right triangle with an angle of 54° and the side opposite this angle is 25.0 cm. We need to find the length of the adjacent side $x$ using the tangent function. 2. **Formula:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** Here, $\theta = 54^\circ$, opposite side = 25.0 cm, and adjacent side = $x$. So, $$\tan(54^\circ) = \frac{25.0}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\tan(54^\circ)$: $$x \times \tan(54^\circ) = 25.0$$ $$\cancel{x} \times \tan(54^\circ) = 25.0 \Rightarrow x = \frac{25.0}{\tan(54^\circ)}$$ 5. **Calculate the value:** Using a calculator, $$\tan(54^\circ) \approx 1.37638$$ $$x = \frac{25.0}{1.37638} \approx 18.16$$ 6. **Final answer:** The length of the adjacent side $x$ is approximately **18.16 cm**.