Geometry

Question Analysis

This question involves Elevation and Depression Angles. The main focus is on using the given altitude (opposite side) and horizontal distance (adjacent side) to find the angle of depression in a right - triangle formed by the plane, the point directly below the plane on the ground, and the observer.

Key Concept Explanation:

The angle of depression from the plane to the observer is equal to the angle of elevation from the observer to the plane. In a right - triangle, we can use the tangent function, where  for an angle  in a right - triangle.

Step - by - Step Solution

1. Let  be the angle of elevation (which is equal to the angle of depression).

The altitude of the plane (opposite side)  feet and the horizontal distance (adjacent side)  feet.

We know that .

Substitute  and  into the formula: .

To find , we take the inverse tangent (arctan) of . So, .

Using a calculator, .

Common Mistakes

1. Confusing the angle of elevation and angle of depression concepts.

2. Using the wrong trigonometric ratio. For example, using

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