As stated above, the "small angle approximation" is not founded in any Code or Standard. Most of us have been introduced to this concept in College. The approximation assumes that rotations and deflections are small enough such that an analysis remains linear and loads and deflections remain uni-directional (so in the case of a spring hanger the load is only vertical).

You can "Google" this idea and find a wealth of information. From http://www.onlinefeasolver.com/articles/nonlinear/ you can get a quick summary.