Final answer:
The distance between two cities with a latitude difference of 45 degrees, 15 minutes, and 20 seconds on Earth with a radius of 4000 miles is approximately 3159.79 miles. After rounding to the nearest hundred, the closest answer is c) 3200 miles.
Step-by-step explanation:
To calculate the distance between two cities with a difference in latitudes of 45 degrees, 15 minutes, and 20 seconds, given a radius of 4000 miles for the Earth, we need to transform the latitude difference into decimal degrees first. Since there are 60 minutes in a degree and 60 seconds in a minute, the conversion to decimal degrees is as follows: 15 minutes = 15/60 degrees = 0.25 degrees. 20 seconds = 20/(60*60) degrees = approx. 0.0056 degrees. So the total latitude difference in decimal degrees is approximately 45.2556 degrees. We know that the Earth's circumference is 2πr (where r is the radius). Since the Earth's circumference is divided into 360 degrees, we can calculate the distance per degree: Earth's circumference = 2 * π * 4000 miles = 25132 miles, Distance per degree of latitude = 25132 miles / 360 degrees = 69.81 miles/degree. Therefore, the distance between two points with a latitude difference of 45.2556 degrees is. Distance = 45.2556 degrees * 69.81 miles/degree = 3159.79 miles. The closest answer to this calculation is c) 3200 miles.