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Finding an arc length

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vping

vping

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Forgot all my structures and I am posed with a problem. I have the height and the with of an arc but not sure of the diameter. Does anyone have a formula for this?
 
Assuming the "width" you refer to is a chord (i.e. the straight line length) try:

r = c*c + 4*h*h / 8*h where r is the radius, h is the height, and c is the length. (c*c = "c squared").

Don't forget to multiply r by 2 for the diameter.
 
Yes the chord! That's what I knew I was missing. This thread sure struck a chord with me.

14" radius was what I was after.

But according to the formula:

R=5.5*5.5+4*.28125*.21825/8*.28125

30.25 + 0.31640625 = 30.56640625

30.56640625/2.25

13.5850694r * 2 = 27.170138 diameter

Close enough for gov't work.
 
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