1. **Stating the problem:** We have a right triangle with a vertical side of length 5.2 m and an angle of 23° adjacent to the base $x$. We want to find the length of the base $x$. 2. **Formula and rules:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, the opposite side to the 23° angle is 5.2 m, and the adjacent side is $x$. 3. **Set up the equation:** $$\tan(23^\circ) = \frac{5.2}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$: $$x \tan(23^\circ) = 5.2$$ Divide both sides by $\tan(23^\circ)$: $$x = \frac{5.2}{\tan(23^\circ)}$$ Show cancellation: $$x = \frac{5.2}{\cancel{\tan(23^\circ)}} \times \frac{1}{\cancel{\tan(23^\circ)}}$$ 5. **Calculate the value:** Using a calculator, $\tan(23^\circ) \approx 0.4245$. $$x = \frac{5.2}{0.4245} \approx 12.24$$ 6. **Final answer:** The length of the base $x$ is approximately **12.24 meters**.