Geometry

Question Analysis

The main focus is using the angle of depression and the height of the mountain to find the horizontal distance from the base of the mountain to the point on the ground. We'll rely on trigonometry within the right - triangle formed by the mountain, the ground, and the line of sight.

Key Concept Explanation

1. Angle of Depression: It's the angle between the horizontal line of sight from an elevated point (top of the mountain) and the line of sight to an object below (point on the ground). In a right - triangle, this angle is related to the trigonometric ratios.

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

Step - by - Step Solution

1. Let the distance from the base of the mountain to the point on the ground be  meters.

The height of the mountain (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 top of the mountain, and using the tangent function