1. **State the problem:** We have a lighthouse beacon 141 feet above water. From point A, the angle of elevation to the beacon is 6°. From point B, closer to the lighthouse, the angle is 12°. We need to find the distance from A to B. 2. **Set up the scenario:** Let the distance from point A to the lighthouse base be $x$ feet. Let the distance from point B to the lighthouse base be $y$ feet. The distance from A to B is then $x - y$. 3. **Use the tangent function:** Since the lighthouse height is opposite and the distance along the water is adjacent, we use: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ From point A: $$\tan(6^\circ) = \frac{141}{x} \implies x = \frac{141}{\tan(6^\circ)}$$ From point B: $$\tan(12^\circ) = \frac{141}{y} \implies y = \frac{141}{\tan(12^\circ)}$$ 4. **Calculate $x$ and $y$:** $$x = \frac{141}{\tan(6^\circ)}$$ $$y = \frac{141}{\tan(12^\circ)}$$ 5. **Find distance from A to B:** $$\text{Distance} = x - y = \frac{141}{\tan(6^\circ)} - \frac{141}{\tan(12^\circ)}$$ 6. **Evaluate using approximate tangent values:** $$\tan(6^\circ) \approx 0.1051$$ $$\tan(12^\circ) \approx 0.2126$$ So, $$x \approx \frac{141}{0.1051} \approx 1342.53$$ $$y \approx \frac{141}{0.2126} \approx 663.12$$ Distance: $$1342.53 - 663.12 = 679.41$$ 7. **Round to nearest foot:** $$\boxed{679 \text{ feet}}$$ This is the distance from point A to point B along the shore.