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June 8th, 2018, 01:31 AM  #1 
Newbie Joined: Jun 2018 From: Idaho Posts: 2 Thanks: 1  Need to calculate the length of an arc
Hello, Need to make an arc that is 16' wide at the base, and rises 12" in the centre. It'll be a perfectly curved arc. I need to know what the length of the beam for the arc should be. I looked up formulas online, but they all want the degree of the arc, but I won't have that until I build it. Would very much appreciate the help. 
June 8th, 2018, 01:58 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond 
Using the information found here, calculate the radius of the circle that contains the arc. Can you proceed from there?

June 8th, 2018, 02:13 AM  #3 
Newbie Joined: Jun 2018 From: Idaho Posts: 2 Thanks: 1 
I believe so. I'll give it a shot. Thank you.

June 8th, 2018, 03:07 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 828 Thanks: 244 
The full formula to find the radius is given in 1 in the sketch. I was working in inches for accuracy. This leads to a radius of 390" or 32' 6". But you probably don't have access to the centre of the circle. Here are two ways to proceed for setting out your arch. First you can use the exact formula and work horizontal distances up from the springings. Or you can use the approximate inverted formula and dip down from a string line stretched tightly across the gap. This is shown in 2. I calculate the maximum error in using the approximate formula is 0.2". If this is acceptable this is a much easier method to implement. 

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arc, calculate, construction, geometry, length, math 
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