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, r2 = (r-h)2 + (L/2)2 Hence r2 = r2 - 2rh + h2 + L2/4 Therefore 2rh = (4h2 + L2)/4 and hence

Cheers
Chris