Geometry

Question Analysis

The main focus of this problem is to use the angle formed by the rope with the ground (angle of elevation) and the length of the rope (hypotenuse) to find the horizontal distance from the building to the point where the rope touches the ground (adjacent side) using trigonometric functions.

Key Concept Explanation

1. Angle of Elevation: In this context, it is the angle between the horizontal ground and the rope.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . Since we know the hypotenuse and want to find the adjacent side, the cosine function is appropriate.

Step - by - Step Solution

1. Let the distance from the building to the point where the rope touches the ground be  feet.

The length of the rope (hypotenuse)  feet and the angle of elevation .

Using the cosine function