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Pythagorean Theorem


Pythagorean Theorem

I understand that the pythagorean theorem is A^2+B^2-C^2. However, I heard that there was a short cut to doing it. It goes something like...

S- shortleg, S- longleg, S(squareroot of)3. It only works for special triangles, I think that one is the 45, 45, 90 triangle. There is also a short cut for the 30, 60, 90 triangle. I was wondering if someone could explain both of them to me. I really want to understand this. Thank you.

On 4/4/2003 11:35:44 AM, Debbie33 wrote:
>I understand that the
>pythagorean theorem is
>A^2+B^2-C^2. However, I heard
>that there was a short cut to
>doing it. It goes something
>S- shortleg, S- longleg,
>S(squareroot of)3. It only
>works for special triangles, I
>think that one is the 45, 45,
>90 triangle. There is also a
>short cut for the 30, 60, 90
>triangle. I was wondering if
>someone could explain both of
>them to me. I really want to
>understand this. Thank you.

There is no "shortcut".

The reason it only works for "special triangles" is because each "shortcut" only works for a SINGLE triangle.

The so-called "shortcut" is simply a coincidentally simply solution to the Pythagorean theorem, the classic case being the 3,4,5 triangle. That solution only works with other similar triangles.

A 45� right triangle has sides 1,1, sqrt(2), which are the solutions to the equation and only work with 45� right triangles. 1,2, sqrt(3) ONLY works with 60� right triangles, because that's the solution for that triangle and does not work for any other triangle.


Eden.....about two years ago, I devised a simple shortcut that I call my "Slide Rule". Please go to YouTube and watch my video to see for yourself. It allows you to estimate the length of the hypotenuse from the known leg lengths and the answer is always within +/- 5% of what the Pythagorean Theorem would provide. It's so easy to learn, in fact, that, with just a little practice, you can learn to do it "in your Head" for ANY triangle, WITHOUT a calculator!!! The video's about 10 minutes long......

A Pythagorean Shortcut - YouTube



Note that the original post, and Eden's reply, were about 14 years ago.

Debbie's account is deactivated, and I haven't seen Eden around for some time.

Nevertheless, yours is a nice video of an impressive method.


I have an easy to use shortcut for you Debbie. Just go to my YouTube video and see just how easy it is for yourself......

A Pythagorean Shortcut - YouTube


Tom, your video impressed me. I've bookmarked it in order to clarify some details... a but a bit later.

I wonder is it your own method?


Kathi Leroy The numbers are squared, added and then the the square root is taken - oh wait that is Pythagorean theorem. Essentially this is  normalized to a base one to get the multiplication factor . Eg SQRT(0.57^2+1^2) = 1.15 and in the box in the "slide rule" the value is rounded up to 1.2. Another one is SQRT(0.32^2+1^2) = 1.04 rounded up to 1.1 - perhaps a graph will have less errors as the discrete jumps will be eliminated. Nothing special here.

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