Geometry

Question Analysis

The main focus of this problem is using the angle of depression from the building to the car and the height of the building to determine the horizontal distance from the base of the building to the car. We'll work with trigonometry in the right - triangle formed by the building, the street, 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 building) and the line of sight to an object below (the car). In a right - triangle, this angle 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 building (opposite side) and needing to find the adjacent side (distance of the car from the base of the building), the tangent function is relevant.

Step - by - Step Solution

1. Let the distance of the car from the base of the building be  meters.

The height of the building (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 building, and using the tangent function

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