Is the Circle Division Math for the Stator Correct?

[MacLaddy]

Not a homework question, I was just hoping someone could assist me with understanding some math. Actually, more accurately, I was wondering if someone could double check the math on the following website.

http://www.otherpower.com/statormold.shtml

If you scroll down you will see some explanations on how to accurately divide the circle into nine equal parts, but I believe he is doing it incorrectly. See where the "Sides, Angles, and Sines" paper is shown. Seems odd that he would be using the $$\sin20\deg$$ when it is $$40\deg$$.

Wouldn't you just do the following

$$\frac{\pi12}{9}~=~4.188...$$

Thanks for any input you can offer. I have been considering taking up this project, but if the math is wrong I may not...

 

[MacLaddy]

Well, I digress. I realized that I needed to figure out the "chord" for the angle, as it will not follow the arc. So I used the formula $$c~=~r\sqrt{2-2cos40}$$. That gave the same answer that he was coming up with by just multiplying $$\sin20~by~12.$$

I apologize if I posted this in the wrong section, it just seemed appropriate here due to the subject matter.

Apparently I'm missing something in my trig knowledge.