Geometry

Question Analysis

The main focus of this problem is to use the angle of elevation and the horizontal distance from the point on the ground to the base of the building to find the height of the building. We will utilize trigonometric functions in the right - triangle formed by the building, the ground, and the line of sight.

Key Concept Explanation

1. Angle of Elevation: It is the angle between the horizontal line of sight from a point on the ground and the line of sight to an object above the horizontal, here, the top of the building.

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

Step - by - Step Solution

1. Let the height of the building be  meters.

The distance from the point to the base of the building (adjacent side)  meters and the angle of elevation .

Using the tangent function