1. **Problem statement:** From a tower 32 m high, a car is observed at an angle of depression of 55 degrees. We need to find the horizontal distance of the car from the base of the tower. 2. **Formula and explanation:** The angle of depression from the top of the tower to the car forms a right triangle where: - The height of the tower is the opposite side to the angle. - The distance from the tower to the car is the adjacent side. We use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the values:** $$\tan(55^\circ) = \frac{32}{d}$$ where $d$ is the distance from the tower to the car. 4. **Solve for $d$:** $$d = \frac{32}{\tan(55^\circ)}$$ 5. **Calculate the value:** Using $\tan(55^\circ) \approx 1.4281$, $$d = \frac{32}{1.4281} \approx 22.4$$ 6. **Answer:** The car is approximately 22.4 meters from the base of the tower.