Right Angled Traingle

[aplavakarthik]

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?

[pgkkumar]

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.

[Tani]

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.