The Geometry of Right Triangles begins the study of Trigonometry. It begins with the geometric definitions of the three main trig functions. Some instructors prefer to begin with the unit circle approach and then proceed to the right triangle approach. We chose to put this lesson before Unit Circle – Part I and Part II, though it could be done afterward. It gives a conceptual introduction to the inverse trig functions, enough to be able to solve right triangles and the focus here is on the solving process. A fuller, more formal treatment of inverse trig functions is given in Inverse Sine and Inverse Cosine Functions, with further details of the domain and range of the inverse trig functions given in Domain and Range of Trig and Inverse Trig Functions.
It is not the intent of this lesson to discuss the similarity of triangles and the fact that the geometric definition is well-defined.