Right Triangles

Date: 3/30/96 at 12:19:29
From: Anonymous
Subject: Right Triangles

Is there an easy way to remember the different right triangles and how 
to find the lengths of missing sides?  I already know that in any right 
triangle  (a*a) + (b*b) = (c*c)

Date: 3/30/96 at 22:45:30
From: Doctor Jodi
Subject: Re: Right Triangles

Hi there! Well, there are a LOT of different right triangles.  In fact, 
there are INFINITELY MANY right triangles.  So, no, I don't think 
*anyone* could remember all of them.

If you want to know more about Pythagorean triples, here's a cool 
trick I stole from 

     http://www.maths.uts.edu.au/number/triples.html   :
______

Here is an unusual way to find Pythagorean triples. Use some doodle 
paper to make your own example.

       Take any two fractions whose product is 2.     | 3/2, 4/3
       Add 2 to each number.                          | 7/2, 10/3
       Cross multiply to get integers a, b in the 
          same ratio.                                 | 21, 20
       Calculate a^2 + b^2.                           | 21^2+20^2
                                                      | = 441 + 400 = 841
       Take the square root, and call it c.           | sqrt(841) = 29

It always happens that c is an integer, so a, b, and c give a Pythagorean 
triple. (In the example here, we have found the Pythagorean triple 20, 
21 and 29.) 
______

If you already have two numbers of a Pythagorean triple and you want to 
find the other, you can use the Pythagorean formula (a^2 + b^2 = c^2).  
Any ideas on how you could figure out whether the 2 numbers you already 
have are the hypotenuse or one of the other sides?
 
Write back if you have more questions!

-Doctor Jodi,  The Math Forum