1. **State the problem:** A man’s eyes are 1.75 m above sea level and he can barely see the top of a lighthouse 20 km away. We need to find the elevation of the lighthouse top above sea level. 2. **Understand the scenario:** The Earth’s curvature limits the line of sight. The distance to the horizon from a height $h$ (in meters) is approximately $d = \sqrt{2Rh}$ where $R$ is Earth’s radius (~6,371,000 m). 3. **Calculate the horizon distance for the man:** $$d_{man} = \sqrt{2 \times 6,371,000 \times 1.75} = \sqrt{22,298,500} \approx 4723.3 \text{ m} = 4.7233 \text{ km}$$ 4. **Calculate the horizon distance for the lighthouse top:** Let the lighthouse height above sea level be $h_{lighthouse}$. The total distance between man and lighthouse is 20 km, so: $$d_{man} + d_{lighthouse} = 20,000 \text{ m}$$ $$d_{lighthouse} = 20,000 - 4,723.3 = 15,276.7 \text{ m}$$ 5. **Find the lighthouse height:** $$d_{lighthouse} = \sqrt{2Rh_{lighthouse}}$$ Square both sides: $$d_{lighthouse}^2 = 2Rh_{lighthouse}$$ Solve for $h_{lighthouse}$: $$h_{lighthouse} = \frac{d_{lighthouse}^2}{2R} = \frac{(15,276.7)^2}{2 \times 6,371,000}$$ Calculate numerator: $$15,276.7^2 = 233,386,000$$ Calculate denominator: $$2 \times 6,371,000 = 12,742,000$$ Calculate height: $$h_{lighthouse} = \frac{233,386,000}{12,742,000} \approx 18.3 \text{ m}$$ 6. **Add the man’s eye height to get total elevation:** $$\text{Elevation} = h_{lighthouse} + 1.75 = 18.3 + 1.75 = 20.05 \text{ m}$$ 7. **Conclusion:** The elevation of the lighthouse top above sea level is approximately **20 m**. **Final answer:** 20 m