Jim,

Welcome back...Your question is a good one. 

If you are given one leg of a right triangle, 'a', you can find the other sides by using this formula:

1. If 'a' is odd, square a and find 2 consecutive numbers that add to equal it.  This will be the other leg and the hypotenuse.
   
2. If 'a' is even, divide a by 2, then square this result.  The two numbers on either side will be the other sides.  (One a leg, the other a hypotenuse.)

Ex [1]  If one leg of a right triangle is 11, find the hypotenuse.

1. Since 11 is odd, square 11 and we get 121.
   
2. Find 2 consecutive numbers that add to equal 121.
   
3. 60 + 61 = 121.  So the other leg is 60 and the hypotenuse is 61.

Ex [2]  If one leg of a right triangle is 12, find the other leg.

1. Since 12 is even, divide by 2 then square it.
   
2. 12/2 = 6.  6^2 = 36.  The two numbers on both sides of 36 are 35 and 37.  The other leg is 35, and the hypotenuse is 37.

I hope this helps.

In the near future there will be a section devoted to trigonometry.  The address will be:  www.math-magic.com/trig.htm.  Keep in mind it will be a little while before this section comes up.

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