1. **State the problem:** Solve for $x$ in the equation $$\frac{x \cdot \tan(49.2)}{\tan(49.2)} = \frac{18}{\tan(49.2)}.$$ 2. **Simplify the left side:** Since $\tan(49.2)$ appears in both numerator and denominator, they cancel out. $$\frac{x \cdot \tan(49.2)}{\tan(49.2)} = x \cdot \frac{\cancel{\tan(49.2)}}{\cancel{\tan(49.2)}} = x.$$ 3. **Rewrite the equation:** Now the equation is $$x = \frac{18}{\tan(49.2)}.$$ 4. **Calculate $\tan(49.2)$:** Using a calculator, $$\tan(49.2^\circ) \approx 1.1504.$$ 5. **Substitute and solve for $x$:** $$x = \frac{18}{1.1504} \approx 15.64.$$ 6. **Final answer:** $$\boxed{x \approx 15.64}.$$