Yes. It doesn't just mainly focus on right triangles. For instance, there's the law of cosines and the law of sines that are used for non-right triangles and are considered trigonometry.
Law of cosines:
Does trigonometry apply to all triangles?
As for as I know, yes.
Oblique triangles, for instance, can be manipulated with the law of cosines.
An example of one law.
a^2 = b^2 + c^2 - 2bc cos(alpha)
Yes, it applies to all triangles.