Geometry

Question Analysis

The main focus of this problem is to use the angle of depression from the top of the tower to a car and the height of the tower to determine the horizontal distance from the base of the tower to the car. We will apply trigonometric concepts within the right - triangle formed by the tower, the ground, and the line of sight to the car.

Key Concept Explanation

1. Angle of Depression: It is the angle between the horizontal line of sight from an elevated point (top of the tower) and the line of sight to an object below (the car). In a right - triangle context, it helps establish relationships between the sides of the triangle.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . Given the height of the tower (opposite side) and needing to find the adjacent side (distance from the base of the tower to the car), the tangent function is appropriate.

Step - by - Step Solution

1. Let the distance from the base of the tower to the car be  meters.

The height of the tower (opposite side)  meters and the angle of depression .

Since the angle of depression is equal to the angle of elevation from the car to the top of the tower, and using the tangent function