**Problem Statement:**An airplane pilot finds the measure of the angle of depression of the edge of the runway to be 47°. If the altitude of the plane is 550 feet, what is the distance from a point on the ground directly below the plane to the edge of the runway?**Diagram Explanation:**The diagram illustrates a right triangle formed by the altitude of the plane (550 feet) as the opposite side, the distance (x) on the ground from the point directly below the plane to the edge of the runway as the adjacent side, and the hypotenuse as the line of sight from the airplane to the runway edge.**Options for Distance (x):**- \( x = 512.9 \, \text{ft} \)- \( x = 589.8 \, \text{ft} \)- \( x = 752.0 \, \text{ft} \)- \( x = 806.5 \, \text{ft} \)**Solution Approach:**To find the distance x, we can use the tangent function for the angle of depression:\[ \tan(47^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{550}{x} \]Solve for x:\[ x = \frac{550}{\tan(47^\circ)} \]Calculate this value to determine which option is correct.**Educational Context:**This problem is a practical application of trigonometry, demonstrating how angles of depression can be used to calculate distances in aviation contexts.

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An airplane pilot finds the measure of the angle of depression of the edge of the runway to be 47°. If the altitude of the plane is 550 feet, what is the distance from a point on the ground directly below the plane to the edge of the runway? 550 ft

An airplane pilot finds the measure of the angle of depression of the edge of the runway to be 47°. If the altitude of the plane is 550 feet, what is the distance from a point on the ground directly below the plane to the edge of the runway? 550 ft

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

**Problem Statement:**

An airplane pilot finds the measure of the angle of depression of the edge of the runway to be 47°. If the altitude of the plane is 550 feet, what is the distance from a point on the ground directly below the plane to the edge of the runway?

**Diagram Explanation:**

The diagram illustrates a right triangle formed by the altitude of the plane (550 feet) as the opposite side, the distance (x) on the ground from the point directly below the plane to the edge of the runway as the adjacent side, and the hypotenuse as the line of sight from the airplane to the runway edge.

**Options for Distance (x):**

- \( x = 512.9 \, \text{ft} \)
- \( x = 589.8 \, \text{ft} \)
- \( x = 752.0 \, \text{ft} \)
- \( x = 806.5 \, \text{ft} \)

**Solution Approach:**

To find the distance x, we can use the tangent function for the angle of depression:
\[ \tan(47^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{550}{x} \]

Solve for x:
\[ x = \frac{550}{\tan(47^\circ)} \]

Calculate this value to determine which option is correct.

**Educational Context:**

This problem is a practical application of trigonometry, demonstrating how angles of depression can be used to calculate distances in aviation contexts.

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