The side lengths of a triangle are consecutive integers.
The largest interior angle is twice the smallest.

What are the side lengths of the triangle?

There's a rule I 'learned' but probably didn't properly as I know about it but can't always apply it, the Sine Rule! 

No that's fine, but it only takes into account the side and opposite angle.  Cosine Rule!  That was another, probably not so well remembered either but definitely related.

The obvious seemed to be a 3,4,5 right angled!  Tried it in a CAD application :  
I took it back to Excel having to battle 'Degrees' against 'Radians' I arrived at a 4,5,6.


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Might I share a thought?
One which is quite erroneous! 

Having arrived at the 4,5,6 solution I wondered about that 3,4,5 triangle.  Yes it was there! Bisect the side '6' to the opposite angle!  Um? That line is not 4!

Note: I did play with this in a CAD program which reinforced my Sin/Cos Rule thoughts.

Thanks Jer

Posted by brianjn on 2009-03-06 03:33:34