1. **Problem Statement:** You are at the top of a watchtower 100 feet above sea level. The angle of depression to a ship in the water is 25 degrees. You need to find the distance $x$ from the top of the watchtower to the ship. 2. **Understanding the scenario:** The angle of depression is the angle between the horizontal line from your eye level and the line of sight to the ship. This angle is 25 degrees. 3. **Diagram and triangle:** The watchtower height is 100 feet (vertical side). The distance $x$ is the hypotenuse of the right triangle formed by the watchtower height and the horizontal distance to the ship. 4. **Choosing the trigonometric ratio:** The angle given is between the hypotenuse and the horizontal side. The side opposite the angle is the height (100 feet), and the hypotenuse is $x$. 5. **Recall trigonometric ratios:** - $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ 6. Since we know the opposite side (height = 100) and want the hypotenuse ($x$), the appropriate ratio is: $$\sin 25^\circ = \frac{100}{x}$$ 7. **Solve for $x$:** $$x = \frac{100}{\sin 25^\circ}$$ 8. **Calculate $\sin 25^\circ$:** $$\sin 25^\circ \approx 0.4226$$ 9. **Final calculation:** $$x = \frac{100}{0.4226} \approx 236.5$$ 10. **Answer:** The distance from the top of the watchtower to the ship is approximately **236.5 feet**. **Summary:** The correct trigonometric ratio to use is **$\sin \theta$** because it relates the opposite side (height) to the hypotenuse (distance $x$).