How to calculate elevation angle between two GPS coordinates?

Since the distance is "short", I believe you can approximate a flat earth and use Pythagoras's theorem. I use this simplified calculation regularly at work to check accuracy of angles coming out of Laser Rangerfinder units, etc, but typically I look at distances of at most a couple of hundred meters. I guess it depends what accuracy you are looking for - I suggest you use these calculations and compare the results to an online calculator if you can find one. The error in Horizontal angle is about 1 second for points 1852M apart so that can probably be ignored, but my calculations assume a spherical Earth and I'm not sure what error that introduces.

1 minute of arc of Latitude or Longitude at the equator is 1 Nautical Mile = 1852M, so all calculations below assume Latitude and Longitude in Seconds of arc. Except for the COS calculation, which usually wants degrees or Radians.

Distance N-S = ABS(Latitude2-Latitude1) * 1852M

Distance E-W = ABS(Longitude2-Longitude1) * 1852M * COS((Latitude2+Latitude1)/2)

Distance Horizontal = SQRT(Distance N-S * Distance N-S + Distance E-W * Distance E-W)

Distance Vertical = Altitude2 - Altitude1

Then Elevation = ArcTan (Distance Vertical / Distance Horizontal)