Question

Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the

following two cities whose latitudes are given. You may assume that these cities are on
the same basic longitude.
Cincinnati, Ohio (39° 8' 46" N) and Huntsville, Alabama (34° 43'41" N)

Answer 1

308.44 miles

Explanation:

• Cincinnati, Ohio (39° 8' 46" N); and

• Huntsville, Alabama (34° 43'41" N)

If the two locations are on the same basic longitude, then they are both on a great circle.

Distance along great circle
`=(\theta)/(360^\circ)X2\pi R`

Where:

`\theta=$Angular difference\\R=Radius of the earth`

Since they are on the same polar axis (North), we subtract.

Angular Difference =39° 8' 46"-34° 43'41"=4°25'5"

Therefore:

`Distance =(4\°25'5'')/(360^\circ)X2*4000*\pi \\=308.44 \:miles`