
Date: Thu, 22 Apr 1999 10:47:12 0600 (CST)
Subject: radius of an arc
Name: Rusty
Who is asking: Other
Level: All
Question:
I need to find the equation for finding the radius of an arc; I know the lenght of the arc (i.e the distance of the line connecting the two ends of the arc) and the height; (i.e the rise of the arc
at its apex,) I had the formula years ago but it has lost me; this would be invalable for work in new homes i.e. where we need to build an "arch" with a rise of 21" between two columns 11 feet apart
thanks
Hi Rusty,
Using the theorem of Pythagoras on the triangle on the right,
r^{2} = (rh)^{2} + (L/2)^{2}
Hence
r^{2} = r^{2}  2rh + h^{2} + L^{2}/4
Therefore
2rh = (4h^{2} + L^{2})/4
and hence


Cheers
Chris

