1. **Problem statement:** A jetliner is flying at 35,000 feet above the ocean. The pilot measures the angle of depression to the coast of an island as 5°. We need to find the horizontal distance from the jetliner to the island's coast in miles. 2. **Understanding the problem:** The angle of depression is the angle between the horizontal line from the pilot's eye and the line of sight to the island. This forms a right triangle where: - The vertical leg is the altitude of the jetliner (35,000 feet). - The angle between the horizontal leg and the hypotenuse (line of sight) is 5°. - The horizontal leg is the distance we want to find. 3. **Formula used:** In a right triangle, the tangent of the angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 5^\circ$, opposite side = 35,000 feet, adjacent side = horizontal distance (d). 4. **Set up the equation:** $$\tan(5^\circ) = \frac{35000}{d}$$ 5. **Solve for $d$:** $$d = \frac{35000}{\tan(5^\circ)}$$ 6. **Calculate $\tan(5^\circ)$:** $$\tan(5^\circ) \approx 0.08749$$ 7. **Calculate $d$ in feet:** $$d = \frac{35000}{0.08749} \approx 400,114.5 \text{ feet}$$ 8. **Convert feet to miles:** Since 1 mile = 5280 feet, $$d = \frac{400114.5}{5280} \approx 75.76 \text{ miles}$$ **Final answer:** The horizontal distance from the jetliner to the coast of the island is approximately **75.76 miles**.