1. **Problem Statement:** Calculate the value of $x$ in a right triangle where one side adjacent to the angle $38^\circ$ is 5.7 m, and $x$ is the side opposite the $38^\circ$ angle. 2. **Formula Used:** 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, $\theta = 38^\circ$, opposite side = $x$, adjacent side = 5.7 m. $$\tan(38^\circ) = \frac{x}{5.7}$$ 4. **Solve for $x$:** $$x = 5.7 \times \tan(38^\circ)$$ 5. **Calculate $\tan(38^\circ)$:** Using a calculator, $$\tan(38^\circ) \approx 0.7813$$ 6. **Find $x$:** $$x = 5.7 \times 0.7813 = 4.4544$$ 7. **Final answer:** Rounded to one decimal place, $$x \approx 4.5 \text{ m}$$