Find the distance between detroit and Atlanta

Question

Detroit: 42 degrees 20 minutes

Atlanta: 33 degrees 45 minutes

Assume that the two cities have the same longitude and find the distance between them in nautical miles. Use 7912 miles for the diameter of earth

Answer 1

If they have the same longitude then they lie on a great circle with radius = 7912/2 = 3956 miles

 

42 degrees 20 minutes = 42.333 degrees

33 degrees 45 minutes = 33.750 degrees

 

The difference in latitude is 

 

42.333 - 33.750 = 8.583 degrees * (pi radians / 180 degrees) = 0.1498 radians

 

The arc length is s=rθ = 3956*0.1498 = 592.6 miles