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,...
Related questions
Question
(If the actual diagram was to be inserted in an educational website, mention the placeholder for the diagram link or provide an alt text description.)
#### Calculation
To find the angle \( x \), we use the tangent function from trigonometry, which relates the angles to the ratios of the opposite sides of a right-angled triangle.
**Formula**:
\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \]
In this scenario, the opposite side is the distance north of the airport (114 miles), and the adjacent side is the distance east of the airport (184 miles).
\[ \tan(x) = \frac{114}{184} \]
Now calculate the angle \( x \):
\[ x = \tan^{-1}\left(\frac{114}{184}\right) \]
\[ x \approx 31.7^\circ \]
Therefore, the pilot needs to turn approximately 31.7 degrees to fly directly towards the airport.
#### Answer Input
A simple input field is provided for students to enter their calculated angle:
\[ x = \_\_\_\text{°} \]
Buttons:
- **Submit Answer**: To submit the calculated angle.
- **Options**: For additional help or resetting the problem.
---
### Educational Objectives
- **Learning Trigonometric Functions**: Understanding the application of the tangent function in real-life navigation scenarios.
- **Practical Geometry and Angle Calculation**: Enhancing problem-solving skills associated with geometry and angles.
#### Footer Information
© 2022 McGraw Hill LLC. All Rights Reserved.
For further assistance or additional problems, refer to the Terms of Use and Privacy Center](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14a97047-56a8-420b-97d8-c66168d5d651%2F0279ca98-47b9-430b-855b-39dfc199acef%2Fbw5t8j7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Aircraft Navigation Angle Calculation
A plane is located 114 miles north and 184 miles east of an airport. To determine the angle \( x \) that the pilot should turn in order to fly directly to the airport, we need to find the angle to the nearest tenth of a degree.
#### Problem Statement
- **Coordinates of the plane relative to the airport:**
- North: 114 miles
- East: 184 miles
#### Diagram
The diagram provided illustrates the position of the plane relative to the airport, showcasing the north (N), south (S), east (E), and west (W) directions. The airplane's current position is shown as being 114 miles north and 184 miles east of the airport.
(If the actual diagram was to be inserted in an educational website, mention the placeholder for the diagram link or provide an alt text description.)
#### Calculation
To find the angle \( x \), we use the tangent function from trigonometry, which relates the angles to the ratios of the opposite sides of a right-angled triangle.
**Formula**:
\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \]
In this scenario, the opposite side is the distance north of the airport (114 miles), and the adjacent side is the distance east of the airport (184 miles).
\[ \tan(x) = \frac{114}{184} \]
Now calculate the angle \( x \):
\[ x = \tan^{-1}\left(\frac{114}{184}\right) \]
\[ x \approx 31.7^\circ \]
Therefore, the pilot needs to turn approximately 31.7 degrees to fly directly towards the airport.
#### Answer Input
A simple input field is provided for students to enter their calculated angle:
\[ x = \_\_\_\text{°} \]
Buttons:
- **Submit Answer**: To submit the calculated angle.
- **Options**: For additional help or resetting the problem.
---
### Educational Objectives
- **Learning Trigonometric Functions**: Understanding the application of the tangent function in real-life navigation scenarios.
- **Practical Geometry and Angle Calculation**: Enhancing problem-solving skills associated with geometry and angles.
#### Footer Information
© 2022 McGraw Hill LLC. All Rights Reserved.
For further assistance or additional problems, refer to the Terms of Use and Privacy Center
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