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May 2nd, 2019, 07:26 PM  #11 
Newbie Joined: May 2019 From: Australia Posts: 7 Thanks: 0 
What I'm trying to ascertain is this. A lot depends on getting this calculation right, so I thought I would ask someone who knows. Let's make some assumptions to avoid further discussion over the accuracy of my figures. Let's assume that all of my figures, Arc length, Arc Height, etc are 100% accurate. Given that I only have this information Arc Length and Arc Height, I cannot see how one could realistically calculate the Chord Length. But for some reason the spreadsheet I showed you does this (so I thought it must be an estimate, or it makes some assumption). I believe this because a circle with a smaller radius with an Arc Height of 10cm for example, and a circle with a larger radius with an Arc Height of 10cm, given the same Arc Length for both examples, would give me a different Chord Length! Am I right in assuming this, or am I getting confused? I'm not trying to trick anyone here. I'm simply implying that there's something that I probably don't know about Chord Math. So I'm asking yourself if my assumptions above are right or am I failing to consider something? Thanks for your attention to this. I'm probably not being clear so I have tried to clarify things above. Last edited by skipjack; May 2nd, 2019 at 08:29 PM. 
May 2nd, 2019, 08:39 PM  #12 
Global Moderator Joined: Dec 2006 Posts: 20,623 Thanks: 2076 
There may well be shorter chord lengths that initially look possible, but I suspect they turn out to correspond to an arc that is more than half of the circle that it's part of. The spreadsheet is probably finding the largest possible chord length, as I suggested earlier.

May 2nd, 2019, 11:15 PM  #13  
Newbie Joined: May 2019 From: Australia Posts: 7 Thanks: 0  Quote:
The geometry in making a fancy tent is harder than I thought.  
May 3rd, 2019, 02:26 AM  #14  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
Let us be quite clear that solution is possible, though the best way depends upon the numbers. If you look at my sketch you will see there are 5 basic quantities. (Yes, the spreadsheet adds some more, but these are just two or more of the basic ones added up.) There are also three basic (independent) equations connecting these 5 quantities. Thus, supplying any two of these quantities leaves 3 to be determined (by the 3 equations). Note I have used the half chord and half arc as it make things simpler. In construction, to the accuracy of available construction theodolites, it is normal to make the approximation that for full chord or arc lengths less than R/20 the approximation sin(θ) = θ may be made. Last edited by skipjack; May 3rd, 2019 at 05:53 AM. Reason: add sketch  
May 3rd, 2019, 06:37 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 20,623 Thanks: 2076 
For the figures that dominover supplied, your "arc length less than R/20" condition isn't satisfied.

May 3rd, 2019, 08:57 AM  #16  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
Nevertheless the approximation is often very useful and I doubt the ability of the OP to measure the dimensions quoted to the accuracy quoted.  
May 10th, 2019, 04:09 AM  #17 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  In case anyone doubts whether this is possible, here is an extract from a junior school geometry textbook. Note theorem 32 There is one circle and only one circle that passes through three given points not in the same straight line. So it is clear that taking two of these points as the endpoints of the chord and one other on the arc fully defines the one and only circular curve available. The rest of the extract shows constructions to find this circle and centre. Last edited by skipjack; May 11th, 2019 at 10:59 PM. 
May 11th, 2019, 01:39 PM  #18  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
Of course the roof is not a plane figure, but coneshaped. Last edited by skipjack; May 11th, 2019 at 11:01 PM.  

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arc, chord, finding, height, length 
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