Geometry

Question Analysis

The main focus of this problem is to use the horizontal distance from the drone's starting point to the tree and the height of the tree to find the minimum angle of elevation the drone must have to avoid hitting the tree. We will apply trigonometric concepts in the right - triangle formed by the drone's path, the ground, and the height of the tree.

Key Concept Explanation

1. Angle of Elevation: It is the angle between the horizontal line (where the drone starts) and the line of the drone's path as it ascends. In a right - triangle, this angle relates the opposite side (height of the tree) and the adjacent side (horizontal distance from the drone to the tree) through trigonometric functions.

2. Trigonometric Functions in Right - Triangles: For an acute angle in a right - triangle, . This formula will be used to calculate the angle of elevation.

Step - by - Step Solution

1. Let the height of the tree be feet and the horizontal distance from the drone to the tree be feet.

We know that , where is the angle of elevation.

Substitute and into the formula: .

To find , we take the inverse tangent (arctan) of 0.3. So,

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