Expert: Paul Klarreich - 10/1/2006

Question
I have a right triagle. Two sides are 21'7".  I think the long side is 30'6".

I think the formula is square root of Asquared + Bsquared.


Answer
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mike Asks in Category Advanced Math ...
 
Subject:  triangle side length
Private:  no
 
Question:  I have a right triangle. Two sides are 21'7".  I think the long side is 30'6".

I think the formula is square root of Asquared + Bsquared.
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Hi, Mike,

Yes, it is.  I will write it in 'computer form' as:

a^2 + b^2 = c^2

You want to write your question as:
I have a right triangle. Two legs are 21'7".  I think the hypotenuse is 30'6".
So it is really:
a^2 + a^2 = c^2, since a = b.

Of course, you concluded that if two sides are equal, they must be the legs, because the hypotenuse is always longer than either of them.

This one is a special case -- an ISOSCELES right triangle.  In it, the hypotenuse is equal to one leg times sqrt(2).  [There is also some 45-degree angle stuff, but we can worry about that later.]

So, writing everything in inches (mixed expressions are so 20th century), you have:

a = 21'7" = 259"
c = a sqrt(2) = 259 sqrt(2)
My Windows calculator says:
c = 366.28131265463161763963737957031
or  c ~~ 366 inches, which is indeed 30'6"

[~~ means 'is approximately equal to']

You should find that

c = sqrt(259^2 + 259^2) = sqrt(2*259^2)
 = sqrt(2) sqrt(259^2)
 = sqrt(2) 259, as above.