Geometry

Question Analysis

The main focus of this problem is to determine the minimum angle of elevation a paraglider must have to clear a cliff. We'll use the horizontal distance from the launch point to the cliff and the height of the cliff, applying trigonometry in the right - triangle formed by the paraglider's path, the ground, and the cliff.

Key Concept Explanation

1. Angle of Elevation: It's the angle between the horizontal line at the launch point and the path of the paraglider as it ascends. In the right - triangle, this angle connects the opposite side (height of the cliff) and the adjacent side (horizontal distance from the launch point to the cliff) through trigonometric functions.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, . We'll use this formula to calculate the angle of elevation.

Step - by - Step Solution

1. Let the height of the cliff be  meters and the horizontal distance from the launch point to the cliff be  meters.

We know that , where  is the angle of elevation.

Substitute  and  into the formula: .

To find , we take the inverse tangent (arctan) of

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