Date: Thu, 22 Apr 1999 10:47:12 -0600 (CST)
Subject: radius of an arc

Name: Rusty
Who is asking: Other
Level: All

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


Hi Rusty,

Using the theorem of Pythagoras on the triangle on the right,
r2 = (r-h)2 + (L/2)2

r2 = r2 - 2rh + h2 + L2/4

2rh = (4h2 + L2)/4

and hence


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