With one satellite you get a sphere in 3D space, but if you are on a surface (like that of the Earth), that gets translated into circle.
If you are in a plane in the sky (3D space), then you get a spherical 'location fix'.
If you have lat-long and place it on a pre-canned map, then it's unlikely that most people will be either underground or in the air, and so whatever the surface elevation of the lat-long on the map is, that's most likely (>99% of the time?) where the person is.
At least from a UX/responsiveness perspective, this is probably a good way to do the math. (In the background get a more accurate 3D fix.)