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Jul 31, 2013 at 20:12 comment added whuber It may be worth mentioning that the projection needs to be conformal only at the vertex B where the angle is measured. For instance, any azimuthal projection based at B will work. The flexibility afforded by this wider range of choices may make it easier to find a suitable projection when A or C are far from B.
May 27, 2011 at 16:16 vote accept Sean
May 27, 2011 at 14:31 comment added whuber @Mersey Yes, you are correct. It would make a difference unless the two spheroids were geometrically similar (same shape but different sizes). This is rare. However, in most cases the difference in angles will be so small as to be unimportant--different spheroids usually are, after all, each very good approximations to the earth's surface--but a change from a true sphere to one with a typical flattening (near 1/298) can be noticeable in some cases.
May 27, 2011 at 7:41 comment added MerseyViking would it make a difference if the spheroid used in the projection was different from the original geographic one? My intuition tells me it would, but I'm not near a computer capable of finding out...
May 26, 2011 at 17:57 comment added whuber @Sean I was afraid you would ask that :-). It depends on how accurate you need the angle. I wouldn't worry ordinarily about triangles even tens of kilometers on a side unless the calculation was being done for a surveyor or astronomer. In case the side lengths are measured in multiple degrees--hundreds of kilometers--it's probably worth finding closer points.
May 26, 2011 at 17:52 comment added Sean Thanks, I imagined a projection was needed at some point but wasn't sure if their was some voodoo to use when the coordinates were expressed as angles. Is their general rule for how close A and C should be to B?
May 26, 2011 at 16:06 history answered whuber CC BY-SA 3.0