Quandaries
and Queries 

I am building a wishingwell out of pieces of 2by4. I have included a picture of a miniature version of what I want. There are to be ten 2by4 pieces around the well and I want the circle around the outside of the structure to have a diameter of approximately 3 feet. How long to I cut the 2by4's to build the wishingwell. Thanks, 

Hi Don, Here is the photo you included.
I sketched a topdown view of the first row of 2by4's on a circular base of diameter 3 feet and labeled some points. (The diagram is not to scale.) Since there are 10 pieces of 2by4 and the angle at the center of a circle is 360^{o}, the angle BCA is 36^{o}. Now bisect the angle BCA and extend the side GF of the 2by4 to meet the outside circle at A.
The line segments CH and DF are parallel and the angle HCD is 18^{o}, hence the angle FDA is 18^{o}. Angle DFA is a right angle and hence
The width of a 2by4 is 3.5 inches so
Thus CD = 18  3.68 = 14.32 inches. Now look at triangle HCD. Angle HCD is 18^{o}, and
Thus the length of the 2by4 is 2 4.43 = 8.83 inches. This is approximately 8 and ^{7}/_{8} inches. Harley 

