Setup: you 2 have points on the surface of the Earth that are close to each other, say 30N100W and 30.1N100.2W, in decimal degrees.
Step 1: find the feet latitude/longitude for each point. For latitude, 1 degree is approximately 365,229', and longitude is approximately 365,229'*cos(latitude). [EDIT: well turns out the circumference of 30N is about 30km more than if you were to treat the Earth as a sphere, but that's like a .1% difference, so I'll disregard]
- This makes the first point ~10,956,870' north of the equator, and ~31,629,759' west of there
- The second point is ~10,993,393' north of the equator, and ~31,661,034 west of there
Step 2: good ol' 2-dimensional distance equation gives ~48,083' apart
Step 3: confirm with an online latitude/longitude distance calculator, plugging in the original 30N100W and 30.1N100.2W, and it instead gives ~72,917'!
Surely approximating the surface of a sphere by a plane on such a small area wouldn't be so far off??? So the real question is... why the huge discrepancy?