Hi Anonymous,
It would be easier to answer your question had you asked a specific example, but since you asked a general question, this is the general idea:
Assuming you mean special right triangles, they are 30-60-90 degree triangles and 45-45-90 degree triangles.
They are special because the ratio of their sides is always constant. 
For the 30-60-90 triangle (on the right),
the side opposite the 30-degree angle is always x, a number.
The side opposite the 60-degree angle would always be square root 3 times that number x, and the side opposite the 90-degree angle (the hypotenuse) would always be 2 times that number x.
So if x= 3 for 30-60-90 triangle,
the side opposite the 60-degree angle would be $${\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{3}}$$ < [3 sqrt(3),but the numbers come out white if I write it that way] and the hypotenuse would be 6.
The 45-45-90 triangle works the same way.
If the side facing the 45-degree angle is 4, then the side facing the other 45-degree angle is also 4, and the side facing the 90-degree angle (the hypotenuse) would be $${\mathtt{4}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}}$$
So these triangles are useful in that once you memorize the ratios of the sides, you would be able to find the length of the sides without using trigonometry or the Pythagorean Theorem:)
