Geometry

Question Analysis

This question focuses on using elevation angles and trigonometry to find the height of a mountain. Given the horizontal distance from the climber to the mountain base and the angle of elevation, we need to calculate the vertical height of the mountain.

Key Concept Explanation

We use the tangent function in a right - triangle. In a right - triangle formed by the mountain's height (opposite side), the horizontal distance from the climber to the base (adjacent side), and the line of sight to the mountain top, tangent of an angle is the ratio of the opposite side to the adjacent side, i.e., .

Step - by - Step Solution

1. Let the height of the mountain be .

We know that the adjacent side feet and the angle of elevation .

Since , and , we substitute the values into the formula.

So,

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