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### 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

```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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