Geometry

Question Analysis

The main focus of this problem is to use the angle of elevation and the horizontal distance from the point of observation to the base of the tree to find the height of the tree. We'll apply trigonometric relations in a right - triangle formed by the tree, the ground, and the line of sight.

Key Concept Explanation

1. Angle of Elevation: It is the angle between the horizontal line of sight and the line of sight to an object above the horizontal, in this case, from the point on the ground to the top of the tree.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . When we know the adjacent side (distance from the point to the base of the tree) and want to find the opposite side (height of the tree), the tangent function is useful.

Step - by - Step Solution

1. Let the height of the tree be  feet.

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

Using the tangent function