Geometry

Question Analysis

The main focus of this problem is to use the concept of the angle of elevation in a right - triangle situation. Given the distance from the climber to the base of the mountain (adjacent side) and the angle of elevation, we need to find the height of the mountain (opposite side) by applying trigonometric functions.

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 line.

2. Trigonometric Functions in Right - Triangles:

For an acute angle  in a right - triangle, , , . In problems involving the angle of elevation, the tangent function is often useful when we know the adjacent side and want to find the opposite side.

Step - by - Step Solution

1. Let the height of the mountain be  meters.

We know that the distance from the climber to the base of the mountain (adjacent side)  meters and the angle of elevation .

Since , and here

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