>Yeap, that's good. Many thanks, John.

You're welcome. And thank you for posting this comment on your page:

http://www.cut-the-knot.org/pythagoras/CosLawMolokach.shtml

I have a PWW that is a slight twist on my original post. Rather than solving for cosA and cosB, I took the equation:

c = acosB + bcosA and multiplied both sides by c. Then I envisioned this as the square of side c being equal to the sum of two rectangles drawn off of sides a and b whose widths are c*cosB and c*cosA respectively.

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0Bwc0zPMWJ9wqNDBjZTNlNTYtMjZmZS00ZmE3LTlhMTMtYjRjNWQ1Nzg5YzY4&hl=en&authkey=CIPjm4oB

This is similar to Don McConnell's PWW at:

http://www.cut-the-knot.org/pythagoras/DonMcConnell.shtml

except it avoids the blue rectangular parts (which come out in the ensuing algebra after my diagram). In addition, the drawing of the arcs makes right angle symbols and marking segments congruent unnecessary.

Also, I wonder if you would be willing to write a Java Applet to go along with this PWW.

Consider points A and B fixed and C movable (perhaps only in the direction of side a). If one makes C a right angle, then the rectangles become squares (The Pythagorean Theorem). If one makes C an obtuse angle, then the rectangles become longer than the sides a and b due to the fact that the altitudes intersecting outside the triangle. When this happens also, the rectangles overlap, yet their sum has to be considered in the total for c^2. But I imagine the overlap could just change color or turn black or something.

I have no knowledge of Java or programming in general, but I think it would make for a great applet and something you might take an interest in.

Also, in doing this I knew I had seen something similar and this is when I found Don McConnell's PWW - I actually remember him posting it on the Exchange somewhere this past summer when I began this obsession of mine with proofs...