Geometry

Question Analysis

The main focus is to utilize the angle of depression and the height of the balcony to find the horizontal distance from the point directly below the balcony to point A. We'll work with trigonometry in the right - triangle formed by the balcony, the ground, and the line of sight to point A.

Key Concept Explanation

1. Angle of Depression: It is the angle between the horizontal line of sight from an elevated point (the balcony) and the line of sight to an object below (point A). In a right - triangle, this angle helps establish relationships between the sides of the triangle.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . Given the height of the balcony (opposite side) and needing to find the adjacent side (horizontal distance), the tangent function is relevant.

Step - by - Step Solution

1. Let the horizontal distance from the point directly below the balcony to point A be  meters.

The height of the balcony (opposite side)  meters and the angle of depression .

Since the angle of depression is equal to the angle of elevation from point A to the balcony, and using the tangent function

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