Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises: 52

Answer

The airplane needs to fly a horizontal distance of 42,642 feet to be directly over the tree.

Work Step by Step

We can convert the angle to degrees: $\theta = 13^{\circ}50' = (13+\frac{50}{60})^{\circ} = 13.833^{\circ}$ Let $h$ be the height of the airplane. We can use $h$ and $\theta$ to find the horizontal distance $d$ the airplane must fly: $\frac{h}{d} = tan(\theta)$ $d = \frac{h}{tan~\theta}$ $d = \frac{10,500~ft}{tan~(13.833^{\circ})}$ $d = 42,642~ft$ The airplane needs to fly a horizontal distance of 42,642 feet to be directly over the tree.
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