An equilateral triangle lies with its three vertices at respective distances from the origin as 1, 2 and 3 units. What is the length of each side of the triangle?

I drew this, pencil and paper as a sketch.  I had the feeling that there were two solutions by the nature of the sketch.

I drew this up in a CAD program with some measure of good luck and reiteration.  Looks good.  I can measure the angles and the lengths; now my settings did not allow me to precisely locate the coords and so my measurements are not properly reconciled.

My diagram uses the closest vertex to the origin as  (0,1).  There after it matters little except that the (2,y) is in either the 3rd or 4th quadrant.

Around the (0,1) point I have angles of 69, 60 and 51. Now I have two measurements which are identical and one which is less by one. These are just below 250, er ... 2.5 units.

When I first saw this I was intrigued but could fathom this.  I suspect polar coords, and they are not in my tool box.

Posted by brianjn on 2007-09-05 09:50:22