1. **State the problem:** We need to find the depth of a lunar crater given the length of its shadow and the angle of elevation of the sun. 2. **Identify the right triangle:** The shadow length is the adjacent side to the angle of elevation $48^\circ$, and the crater depth is the opposite side. 3. **Use the tangent function:** In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. 4. **Set up the equation:** Let the depth be $d$. Then $$\tan(48^\circ) = \frac{d}{400}$$ 5. **Solve for $d$:** $$d = 400 \times \tan(48^\circ)$$ 6. **Calculate the value:** Using a calculator, $$\tan(48^\circ) \approx 1.1106$$ 7. **Final depth:** $$d \approx 400 \times 1.1106 = 444.24$$ **Answer:** The depth of the crater is approximately 444.24 meters.