1. **State the problem:** A boat is approaching a lighthouse with a beacon 137137 feet above water. The angle of elevation from the boat to the beacon is 15 degrees. We need to find the horizontal distance from the boat to the lighthouse. 2. **Formula used:** We use the tangent of the angle of elevation, which relates the height and horizontal distance: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{height}}{\text{distance}}$$ 3. **Apply the formula:** Let $d$ be the horizontal distance. Then: $$\tan(15^\circ) = \frac{137137}{d}$$ 4. **Solve for $d$:** $$d = \frac{137137}{\tan(15^\circ)}$$ 5. **Calculate $\tan(15^\circ)$:** $$\tan(15^\circ) \approx 0.2679$$ 6. **Substitute and compute:** $$d = \frac{137137}{0.2679} \approx 511774.3$$ 7. **Final answer:** The horizontal distance from the boat to the lighthouse is approximately **511774.3 feet**.