Geometry

Question Analysis

This question involves Elevation and Depression Angles. The main focus is on using trigonometric functions to find the angle between a rope (hypotenuse) and the ground, given the lengths of the two sides of a right - triangle formed by the tree, the ground, and the rope.

Key Concept Explanation

We use the cosine function in a right - triangle. In a right - triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Step - by - Step Solution

Let the angle the rope makes with the ground be . The length of the rope (hypotenuse)  meters and the distance from the tree to the point where the rope touches the ground (adjacent side)  meters.

We know that .

Substituting the given values, .

To find