Quandaries
and Queries 

Hi. I was constructing my fence and was having some problems trying to do a perfect (or as close as possible) arch. If i know a section of a fence is for example 85 inches wide and I want a 4 inch rise from the top rail how do i figure out the radius?   [ ] [ ] [ ] This would be the fence with the long horizontal line been where the rail is, and the small horizontal line been where i want the top of arch to reach. Thank You Andres 

Hi Andres, I drew a diagram of a section of your fence. C is the center of the circle, r is the radius of the circle, a is half the width of the section and b is the height of the rise. In the example you sent a is ^{85}/_{2} = 42.5 inches and b is 4 inches.
On the diagram, triangle QPC is a right triangle and hence, by Pythagoras' Theorem
That is
Solving for r gives
With your dimensions I get
Penny 

