You can put this solution on YOUR website! What are you talking about?
Are you saying that you don't study other triangles in trig ?
Trig is based on the study of right triangles to begin with but other triangles are studied. If you don't have thorough understanding of right triangles you will not understand how the others work. Plus the right triangle is very important in math it comes up over and over. Can you immediately identify a triangle with sides 9,12 and 15 as a right triangle?
Be patient.
Here is a great article which discusses the topics of trig.
http://oolong.co.uk/trig.htm
Go to the section on "More Triangles"
Or are you saying that you don't study right triangles in history?