1. **State the problem:** We need to find the horizontal distance from the boat to the foot of the cliff. The cliff height is 55 m, and the angle of depression from the top of the cliff to the boat is 26°. 2. **Understand the angle of depression:** The angle of depression is the angle between the horizontal line from the observer's eye (top of the cliff) and the line of sight to the boat. This angle is equal to the angle between the vertical cliff and the horizontal distance to the boat due to alternate interior angles. 3. **Identify the right triangle:** The cliff forms the vertical side (opposite side), the distance from the boat to the foot of the cliff is the horizontal side (adjacent side), and the line of sight is the hypotenuse. 4. **Use the tangent function:** Tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. $$\tan(26^\circ) = \frac{55}{d}$$ where $d$ is the distance from the boat to the foot of the cliff. 5. **Solve for $d$:** $$d = \frac{55}{\tan(26^\circ)}$$ 6. **Calculate the value:** $$\tan(26^\circ) \approx 0.4877$$ $$d = \frac{55}{0.4877} \approx 112.77$$ 7. **Final answer:** The distance from the boat to the foot of the cliff is approximately **112.77 meters**.