1. **State the problem:** A 5.5-foot tall man is standing with the sun shining at an angle of depression of 55°. We need to find the length of his shadow. 2. **Formula and explanation:** The angle of depression from the sun to the tip of the shadow corresponds to the angle between the horizontal ground and the line from the top of the man to the tip of the shadow. We can model this as a right triangle where: - The height of the man is the opposite side to the angle. - The length of the shadow is the adjacent side. Using the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 55^\circ$, opposite = 5.5 feet, adjacent = shadow length $s$. 3. **Set up the equation:** $$\tan(55^\circ) = \frac{5.5}{s}$$ 4. **Solve for $s$:** $$s = \frac{5.5}{\tan(55^\circ)}$$ 5. **Calculate the value:** Using $\tan(55^\circ) \approx 1.4281$, $$s = \frac{5.5}{1.4281} \approx 3.85$$ 6. **Interpretation:** The shadow length is approximately 3.85 feet. **Final answer:** $$\boxed{3.85 \text{ feet}}$$