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Right Angled Traingle

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by aplavakarthik » Tue Aug 16, 2011 2:33 am
If sides of a right triangle are 3,4 and x(length of hypotenuse), we can say by Pythagoras Theorem that x=5. Now my question for any given triangle if length of sides satisfy the Pythagoras Theorem can we call a right triangle.

Eg: given sides of the triangle are 8,6,10. Is it a right triangle?
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by pgkkumar » Tue Aug 16, 2011 2:59 am
Yes. You can use the general formula for Cosine of an angle, given three sides,

Cos A = [(b)^2+ (c)^2-(a)^2]/2bc.

Only for a right triangle with A=90 degrees will this equation become zero. And that is true for any Pythagorean triple.
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by Tani » Tue Aug 16, 2011 8:15 am
And for any multiple of a triple, for example:
3:4:5 6:8:10 12:16:20, etc.

or 5:12:13 10:24:26 15:36:39 etc.
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