How can I calculate central angle of an arc when I only know its sagitta and chord?
I have tried and I am able to calculate the radius from the given info but calculating central angle requires the length of the arc which is also unknown.
Arc central angle from Arc width and height
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$\begingroup$
geometry
circles
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0Yes, it is possible. – 2017-02-08
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0Cool, what would be the formula? – 2017-02-08
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0New to the site; why is the question bad/downvoted? – 2017-02-08
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0"Width and height" of arc? How do you define those? – 2017-02-08
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0@DonAntonio: edited question with proper terminology – 2017-02-08
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0Regarding the downvote, I'd guess it is because your question is lacking context, in this case, your own thoughts on how to solve the problem. This information is important as it tells a potential answerer what your level of understanding is, so that s/he can go from there. It could also be because it isn't clear what you mean by the terms you use. Welcome to the site! :) – 2017-02-08
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0@Lovsovs: Thanks, I edited the question to improve it. – 2017-02-08
1 Answers
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Look at Wikpedia where if $r$ is the radius, $\ell$ is the chord, $s$ is the sagitta it is given $$r=\frac s2 + \frac {\ell^2}{2s}$$ Then you can use the right triangles with the chord and radius to get the angle.