Question

Does the angle-side relationship in triangles correspond with specific triangles or does it apply in all triangles?

Answer 1

Not sure what you mean by "angle-side relationship" in triangles.
The angles and sides are related by the Sine Law and the Cosine Law in trig

If you are looking for something else, have some fun with this:

http://www.mathopenref.com/trianglesideangle.html