The similarity of triangles gives rise to trigonometry. How could we understand that the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for proportions between sides of two triangles, and these proportions allow for the calculations of which we are speaking here. The similarity of triangles is the foundation of trigonometry.
I was asked this question by my Professor. I don't quite understand the question (and English sentence) very well. Because I learned that the ratios of a right triangle is:
$1:1:\sqrt{2}$
where the ratio is order by adjacent : opposite : hypotenus.
So the question is:
How come the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles?