Geometry

Question Analysis

The main focus of this problem is to use the angle of depression and the altitude of the plane (opposite side in a right - triangle) to find the horizontal distance from the point directly below the plane to the observed point on the ground (adjacent side) by applying trigonometric functions.

Key Concept Explanation

1. Angle of Depression: The angle between the horizontal line of sight from an elevated object (the plane) and the line of sight to an object below (the point on the ground). In a right - triangle formed by the plane's altitude, the horizontal distance, and the line of sight, it is related to the trigonometric ratios.

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

Step - by - Step Solution

1. Let the distance from the point directly below the plane to the point on the ground be  meters.

The altitude of the plane (opposite side)  meters and the angle of depression .

Since the angle of depression is equal to the angle of elevation from the point on the ground to the plane, and using the tangent function

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