



 
Mark, In my diagram r is the radius of the circle, c is half the chord length and h is height of the arc above the chord. Triangle ABC is a right triangle and hence, by Pythagoras' theorem
and hence
I changed all your measurements to inches and got
which is 20' 6". I didn't need to use the length of the arc so I decided to check my calculations by using a radius of 245.943 inches to calculate the length of the arc. The length a of the arc is given by
where θ is the angle at the centre of the circle measured in radians. The angle BCA is θ/2 and sin(BCA) = c/r. Hence
Thus θ = 2 × 0.8453 = 1.691 radians. Hence
This is 34' 8" which is not the length you have for the arc. Are you sure the arch is an arc of a circle? Harley  


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