1. **State the problem:** We have a lighthouse 111 feet tall and two points A and B on the water. From A, the angle of elevation to the top of the lighthouse is 8°, and from B (closer to the lighthouse), the angle is 16°. We need to find the distance between points A and B. 2. **Set up the variables and diagram:** Let the horizontal distance from point B to the lighthouse base be $x$ feet. Then the distance from point A to the lighthouse base is $x + d$, where $d$ is the distance from A to B that we want to find. 3. **Use the tangent function for right triangles:** The height of the lighthouse is opposite the angle, and the horizontal distance is adjacent. From point A: $$\tan(8^\circ) = \frac{111}{x + d}$$ From point B: $$\tan(16^\circ) = \frac{111}{x}$$ 4. **Express $x$ from point B's equation:** $$x = \frac{111}{\tan(16^\circ)}$$ 5. **Express $x + d$ from point A's equation:** $$x + d = \frac{111}{\tan(8^\circ)}$$ 6. **Find $d$ by subtracting:** $$d = \frac{111}{\tan(8^\circ)} - \frac{111}{\tan(16^\circ)}$$ 7. **Calculate the tangent values:** $$\tan(8^\circ) \approx 0.1405$$ $$\tan(16^\circ) \approx 0.2867$$ 8. **Calculate each term:** $$\frac{111}{0.1405} \approx 790.0$$ $$\frac{111}{0.2867} \approx 387.3$$ 9. **Calculate $d$:** $$d = 790.0 - 387.3 = 402.7$$ 10. **Answer:** The distance from point A to point B is approximately **402.7 feet**.