If by special right triangles you mean 30,45, or 60 degree triangles, then I would suggest memorization. I don't usually suggest rote memorization but in this case there are only 3 numbers to remember and they show up many times.
30 and 60 are really the same triangle but viewed from opposite ends.
While 45 is the easiest because you can figure it out if you've forgot the components. You just have to know that since the angles are the same 45=45 the length have to be the same.
You could just start with each leg being 1 long. therefore the hypotenuse is sqrt(1^2+1^2)=sqrt(2). But since we want everything to be on a unit triangle we divide by the hypotenuse to get leg lengths of 1/(sqrt(2), which is usually written as sqrt(2)/2.
Here is where it becomes useful to memorize as the lengths are 1/2 and sqrt(3)/2. Where the larger side goes with the larger angle i.e. (60 with sqrt(3)/2).
A easy way to remember the side are to think of them as the roots of 1,2,3 over 2. Where the smallest number goes with the smallest angle.
then you can also add in 0 and 90 degrees to get