Geometry

Question Analysis

The main focus of this problem is to use the angle of depression and the height of the cable car above the ground to find the straight-line distance from the cable car to the point on the ground directly beneath it. We will rely on trigonometry in the right triangle formed by the cable car, the ground, and the line of sight.

Key Concept Explanation

1. Angle of Depression: It is the angle between the horizontal line of sight from an elevated object (the cable car) and the line of sight to an object below (the point on the ground directly beneath). In a right triangle, this angle helps in establishing 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 cable car (opposite side) and needing to find the hypotenuse (straight-line distance from the cable car to the point on the ground), the sine function is relevant.

Step - by - Step Solution

1. Let the straight-line distance from the cable car to the point on the ground be meters.

The height of the cable car (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 cable car, and using the sine function

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