1. **State the problem:** Nicole shines a light from a lighthouse window 250 feet above water. Nick is on a ship 10 feet above water, and the angle of elevation to the light is 3°. We need to find the length of the line of sight (light beam) from the ship to Nicole. 2. **Identify the triangle and variables:** The vertical difference in height between Nicole and Nick is $250 - 10 = 240$ feet. 3. **Use trigonometry:** The angle of elevation is 3°, the opposite side to this angle is 240 feet (height difference), and the hypotenuse is the line of sight $x$ we want to find. 4. **Formula:** In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. 5. **Set up the equation:** $$\sin(3^\circ) = \frac{240}{x}$$ 6. **Solve for $x$:** $$x = \frac{240}{\sin(3^\circ)}$$ 7. **Calculate $\sin(3^\circ)$:** $$\sin(3^\circ) \approx 0.05234$$ 8. **Substitute and compute:** $$x = \frac{240}{0.05234} \approx 4585.7$$ 9. **Answer:** The length of the line of sight is approximately **4585.7 feet**.