1. **State the problem:** A boat is approaching a lighthouse with a beacon 137 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 opposite side (height of the beacon) to the adjacent side (horizontal distance). The formula is: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ where $\theta = 15^\circ$, opposite = 137 feet, and adjacent = horizontal distance $d$. 3. **Set up the equation:** $$\tan(15^\circ) = \frac{137}{d}$$ 4. **Solve for $d$:** $$d = \frac{137}{\tan(15^\circ)}$$ 5. **Calculate $\tan(15^\circ)$:** Using a calculator, $\tan(15^\circ) \approx 0.2679$ 6. **Substitute and compute:** $$d = \frac{137}{0.2679}$$ 7. **Simplify:** $$d \approx 511.3$$ 8. **Answer:** The horizontal distance from the boat to the lighthouse is approximately **511.3 feet**.