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.
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
adjacent opposite hypotenuse
distance and angle
Right, acute, and obtuse...
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.
Plane trigonometry is trigonometry carried out in (on) a plane. This could be contrasted with spherical trigonometry, which is trigonometry carried out on the surface of a sphere. Certainly there are some other more complex forms of trig.
trigonometry deals to triangle while the the geometry on the shape..
The answer depends on what other information is available to you.
An architect who designs a bridge would use trigonometry, among other mathematical techniques.
Some trigonometry mathematicians also worked on other aspects of mathematics. Hope that answers your question.
Students are taught trigonometry so they meet the needs in architecture, astronomy and in other fields because trigonometry is the branch of Maths and maths is being used everywhere.