distance and angle
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
Two types of trigonometry are recognized: planar and spherical. Planar is 2-dimensional, while spherical is 3-dimensional. Though these are different fields, spherical trigonometry is really just an application of planar trigonometry in several planes.
adjacent opposite hypotenuse
Right, acute, and obtuse...
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
Trigonometry based on a unit circle and radians and trigonometry based on a right triangle.
The wording of the question implies that you already have some kinds of trigonometry in mind and wish to know about others. However, you have not communicated which ones you do know about and we cannot guess that. As a result, we would not know whether our answer gives the kinds of trigonometry that you are already aware of or new ones. Consequently, it is not possible to answer the question with the amount of information it contains.
Angles in trigonometry are the same as any other angles. They are a measure of the separation between two lines which meet at a point.
plane trigonometry spherical trigonometry
one-to-oneone-to-manymany-to-onemany-to-manyI hope it helps :D LLe Jiks