The ratio of two sides of one right triangle is the same of the corresponding sides of any its similar triangles.
Call a, b, c the sides of a right triangle and A, B, C the sides of any of its similar triangles.
Then a/b = A/B, which means that this ratio is a constant.
The same for a/c = A/C, and b/c = B/C.
Even, the same is true for the inverses: b/a = B/A; c/b = C/B, and d/a = C/A.
Then, you can define a function for every one of these ratios. Those functions are the trigonometric functions.
