1. **State the problem:** A boat is observing a lighthouse beacon 139 feet above water. The angle of elevation from the boat to the beacon is 11°. We need to find the horizontal distance from the boat to the lighthouse. 2. **Identify the right triangle and variables:** The lighthouse height is the vertical side ($139$ ft), the horizontal distance from the boat to the lighthouse is the adjacent side (let's call it $x$), and the angle of elevation is $11^\circ$. 3. **Use the tangent function:** Tangent relates the opposite side to the adjacent side in a right triangle: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 11^\circ$, opposite = $139$, adjacent = $x$. 4. **Set up the equation:** $$\tan(11^\circ) = \frac{139}{x}$$ 5. **Solve for $x$:** $$x = \frac{139}{\tan(11^\circ)}$$ 6. **Calculate $\tan(11^\circ)$:** Using a calculator, $\tan(11^\circ) \approx 0.19438$ 7. **Substitute and compute:** $$x = \frac{139}{0.19438}$$ 8. **Simplify:** $$x \approx 714.88$$ 9. **Answer:** The horizontal distance from the boat to the lighthouse is approximately **714.88 feet**.