Question

City A is due north of City B. Find the distance between City A​ (north latitude 43 degrees 27 minutes ​N) and City B (latitude 29 degrees 29 minutes N) Round to the nearest integer. Use 3960 miles as the radius of the Earth.

Answer 1

the distance between City A To find the distance between City A (north latitude 43 degrees 27 minutes N) and City B (latitude 29 degrees 29 minutes N), we can use the formula for the distance between two points on a sphere. In this case, we'll use the radius of the Earth as 3960 miles.

STEP BY STEP EXPLANATION

1. Convert the latitude of both cities to decimal degrees:

- City A: 43 degrees 27 minutes = 43 + (27/60) = 43.45 degrees

- City B: 29 degrees 29 minutes = 29 + (29/60) = 29.4833 degrees

2. Calculate the difference in latitude:

- Latitude difference = City A latitude - City B latitude = 43.45 - 29.4833 = 13.9667 degrees

3. Convert the latitude difference to radians:

- Latitude difference in radians = Latitude difference * (pi/180) = 13.9667 * (pi/180)

4. Calculate the distance using the formula:

- Distance = Radius of Earth * Latitude difference in radians = 3960 * (13.9667 * (pi/180))

5. Round the distance to the nearest integer:

- Distance = Round(Distance)

Calculating the above expression, we find that the distance between City A and City B is approximately 960 miles.nd City B is approximately 960 miles.