What does the .NET framework provide, if anything, in the way of classes for performing geometric calculations? For example, calculating the distance between two points (represented as (x,y)) or solving a right triangle's unknown sides or internal angles? (I know that both of those are pretty easily solved; I'm just using those as examples).
If there's nothing built-in does anyone know of any open source or third party libraries that might be helpful?
Well, there are the spatial types in the SQL Server library that might help with some of your needs? (certainly things like distance/area on 2D/3D surfaces). These are intended to be used from TSQL, but as I understand it you should be able to use them in .NET too (since they are just assemblies).
I know the programmer that put together the mathematics library called WW.Math. It is written entirely in C#. I highly recommend it as it is well documented and intuitive to use. It is used extensively in our own 2d/3d engineering software.
Edit: I should mention that the library is not free.