Find the distance between two cities.
Answer to Problem 72E
Explanation of Solution
Given information:
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has a latitude of
Calculation:
Use trigonometry to calculate the distance between two points on the Earth’s surface if they lie on the same meridian and we are given the latitudes of the two points.
The length of an arc subtended by the angle
Also, remember that to convert degrees to radians we multiply by
To convert radians to degrees, we multiply by the reciprocal,
Now, given that the latitude of Memphis, Tennessee, is
Given that the two cities lie on the same meridian and that the radius of the Earth is
We can use the above relationships to calculate the distance between the two cities.
First we calculate the angle,
Next, we convert the angle to radians, so that
Put this into our equation, we get the arc that subtends angle
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning