From city A to city B, a plane flies 850 miles at a bearing of N 58° E. How many miles north and how many miles east has the plane traveled? Round your answer to the nearest mile. The plane traveled 721 miles west and 450 miles north. The plane traveled 450 miles east and 721 miles north. The plane traveled 450 miles north and 721 miles east. The plane traveled 450 miles north and 450 miles east. ➤
From city A to city B, a plane flies 850 miles at a bearing of N 58° E. How many miles north and how many miles east has the plane traveled? Round your answer to the nearest mile. The plane traveled 721 miles west and 450 miles north. The plane traveled 450 miles east and 721 miles north. The plane traveled 450 miles north and 721 miles east. The plane traveled 450 miles north and 450 miles east. ➤
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![### Navigational Problem: Determining North and East Distances Traveled
**Problem Statement:**
From city A to city B, a plane flies 850 miles at a bearing of N 58° E. How many miles north and how many miles east has the plane traveled? Round your answer to the nearest mile.
**Multiple Choice Answers:**
1. The plane traveled 721 miles west and 450 miles north.
2. The plane traveled 450 miles east and 721 miles north.
3. The plane traveled 450 miles north and 721 miles east.
4. The plane traveled 450 miles north and 450 miles east.
### Solution Analysis:
To solve this problem, we need to break down the plane’s journey into its northward and eastward components using trigonometric functions.
Given:
- Total distance traveled (hypotenuse) = 850 miles
- Bearing = N 58° E (which means 58 degrees east of north)
We use sine and cosine to determine the two components:
- Northward Component = \( 850 \times \cos(58°) \)
- Eastward Component = \( 850 \times \sin(58°) \)
1. **Northward Distance:**
\[ 850 \times \cos(58°) \approx 850 \times 0.5299 = 450 \text{ miles} \]
2. **Eastward Distance:**
\[ 850 \times \sin(58°) \approx 850 \times 0.8480 = 721 \text{ miles} \]
Therefore, the distance traveled north is approximately 450 miles and the distance traveled east is approximately 721 miles.
### Correct Answer:
The plane traveled 450 miles north and 721 miles east.
The correct choice is:
- The plane traveled 450 miles north and 721 miles east.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c67c4d0-217c-4e3e-983c-7902447cdce8%2Fae6a1a97-1550-450c-9a0f-0ed2124a4ab4%2Frj3xtfv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Navigational Problem: Determining North and East Distances Traveled
**Problem Statement:**
From city A to city B, a plane flies 850 miles at a bearing of N 58° E. How many miles north and how many miles east has the plane traveled? Round your answer to the nearest mile.
**Multiple Choice Answers:**
1. The plane traveled 721 miles west and 450 miles north.
2. The plane traveled 450 miles east and 721 miles north.
3. The plane traveled 450 miles north and 721 miles east.
4. The plane traveled 450 miles north and 450 miles east.
### Solution Analysis:
To solve this problem, we need to break down the plane’s journey into its northward and eastward components using trigonometric functions.
Given:
- Total distance traveled (hypotenuse) = 850 miles
- Bearing = N 58° E (which means 58 degrees east of north)
We use sine and cosine to determine the two components:
- Northward Component = \( 850 \times \cos(58°) \)
- Eastward Component = \( 850 \times \sin(58°) \)
1. **Northward Distance:**
\[ 850 \times \cos(58°) \approx 850 \times 0.5299 = 450 \text{ miles} \]
2. **Eastward Distance:**
\[ 850 \times \sin(58°) \approx 850 \times 0.8480 = 721 \text{ miles} \]
Therefore, the distance traveled north is approximately 450 miles and the distance traveled east is approximately 721 miles.
### Correct Answer:
The plane traveled 450 miles north and 721 miles east.
The correct choice is:
- The plane traveled 450 miles north and 721 miles east.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning