Question

find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other)
Dallas, Texas Latitude: 32* 47' 39"
Omaha, Nebraska Latitude: 41* 15' 50"

Answer 1

change in latitude = 41:15:50 - 32:47:39
= 8:28:11
= 8.47°

circumference = 2π(4000) = 8000π
use a ratio:
distance/8000π = 8.47/360
distance = 8000π(8.47)/360
= appr 590 miles

or
using the fact that 1 nautical mile = 1 minute on a great circle
8:28:11
= 508.2 minutes of angle
so 508.1 nautical miles, but
1 nm = appr 1.15 statute mile

so 508.2 = 508.2(1.15) miles = appr 584 miles
not bad only a few miles off