Geometry

Question Analysis

The main focus of this problem is to use the angle of elevation and the length of the shadow (adjacent side in a right - triangle) to find the height of the flagpole (opposite side) by applying trigonometric functions.

Key Concept Explanation

1. Angle of Elevation: It is the angle between the horizontal line (ground level) and the line of sight from the tip of the shadow to the top of the flagpole.

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

Step - by - Step Solution

1. Let the height of the flagpole be meters.

The length of the shadow (adjacent side) meters and the angle of elevation .

Using the tangent function , we substitute the values:

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