A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 feet, what is the altitude of the helicopter?
A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 feet, what is the altitude of the helicopter?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:**
A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 feet, what is the altitude of the helicopter?
**Answer:**
To find the altitude of the helicopter, we use the trigonometric function tangent, which relates the angle of depression to the opposite and adjacent sides of the right triangle formed.
\[ \text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Given:
- Angle of depression, \( \theta = 73^\circ \)
- Horizontal distance (adjacent), \( 1200 \) feet
Let the altitude of the helicopter (opposite side of the triangle) be \( x \).
\[ \text{tan}(73^\circ) = \frac{x}{1200} \]
\[ x = 1200 \times \text{tan}(73^\circ) \]
Calculating \( x \) will give the altitude of the helicopter. Be sure to use a calculator to find \( \text{tan}(73^\circ) \) and round your answer to the nearest tenth if necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F409cee4a-60f6-4aa4-afef-be7f51867a9b%2Ff3c0e7ea-6b22-4cde-81b7-cf4b13ec8912%2Fsgemol_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 feet, what is the altitude of the helicopter?
**Answer:**
To find the altitude of the helicopter, we use the trigonometric function tangent, which relates the angle of depression to the opposite and adjacent sides of the right triangle formed.
\[ \text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Given:
- Angle of depression, \( \theta = 73^\circ \)
- Horizontal distance (adjacent), \( 1200 \) feet
Let the altitude of the helicopter (opposite side of the triangle) be \( x \).
\[ \text{tan}(73^\circ) = \frac{x}{1200} \]
\[ x = 1200 \times \text{tan}(73^\circ) \]
Calculating \( x \) will give the altitude of the helicopter. Be sure to use a calculator to find \( \text{tan}(73^\circ) \) and round your answer to the nearest tenth if necessary.
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