What does sin(x), cos(x), tan(x), etc ACTUALLY tell you?

i understand that, e.g., sin(x) is the opposite side of a right triangle divided by the hypotenuse, but why are these functions important? Given the lengths of the triangle i knwo you can compute the angle using one of the inverse trig functions, so is this why its important? I know this is probably a really really silly question but most texts just brush over this