# Prove Pythagorean Identity and area of the triangle using diagram.

Prove the Pythagorean Identity using a diagram? And also prove that Area of triangle = a^s sinC x sinB/ 2 Sin(B+C)?

 galactus Posts: 2,272, Reputation: 1436 Ultra Member #11 May 2, 2009, 08:58 AM
Why would give me a disagree when I was trying to help?. I am not sure what you are after. There are proofs of the Pythagorean theorem all over the internet.
 galactus Posts: 2,272, Reputation: 1436 Ultra Member #12 May 2, 2009, 09:09 AM
Here is a proof I always liked using Differential Equations. I just remembered this one from way back. It can most likely be found on the web as well.

By noting how the change is a side changes the hypoteneuse.

$\frac{da}{dc}=\frac{c}{a}$

Separate variables:

$cdc=ada$

Integrate:

$c^{2}=a^{2}+K$

If a=0, then b=c.

So the constant is $b^{2}$

$a^{2}+b^{2}=c^{2}$

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