Geometry

Question Analysis

The main focus of this problem is to use the angle of depression from the top of the cliff to the boat and the height of the cliff to calculate the horizontal distance between the boat and the base of the cliff. We'll rely on trigonometry within the right - triangle formed by the cliff, the water surface, and the line of sight to the boat.

Key Concept Explanation

1. Angle of Depression: It's the angle between the horizontal line of sight from an elevated point (top of the cliff) and the line of sight to an object below (the boat). In a right - triangle, this angle helps in connecting the sides of the triangle through trigonometric ratios.

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

Step - by - Step Solution

1. Let the distance of the boat from the base of the cliff be  meters.

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

Since the angle of depression is equal to the angle of elevation from the boat to the top of the cliff, and using the tangent function

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