Dear Delissa:
This is a standard problem of spherical trigonometry. Given latitude
and longitude of two points A, B on the sphere, find the distance
(on the sphere) between them. You do this by considering the spherical
triangle ABP, where P is the north pole, and use the formulas for
spherical triangles (they are somewhat similar to the formulas for plane
triangles). Any good book of trigonometry has them. By the way, I learned
this in high school, but this was in Argentina and in the 30's. Another
remark: if the two points are at the same latitude, their shortest
distance IS NOT the arc of parallel (of constant latitude).
Regards Emilio