Given you have a particular arc length, a particular chord length, and given that it is a minor circular arc, there is only one circle you can derive from it. I know this is possible, to derive a sagitta (arc height) from the chord length and the arc length, I'm just not sure as to how. Everything I've read thus far states it's not possible, but being a man of science, this is not an acceptable answer. There is a direct correlation between the arc length and chord length to produce the sagitta, there has to be. If you keep a constant chord length of say.. Ten, and you have an arc length of twelve, or fifteen, or five hundred seventy-six, the sagitta will adjust accordingly, so, this tells me there is a direct correlation. That being said, has anyone solved this? Surely I can't be the first person to pose this question and relentlessly hunt for an answer.
In specific, if I have an arc length of 80, and a chord length of 71, on a minor arc, what is the sagitta?
If I can solve for the sagitta with the two variables (a = arc length, c = chord length), I can solve for radius, diameter, circumference, and more importantly, the angle of the arc.
Thank you for reading, and thank you even more if you can help.
-Dj
In specific, if I have an arc length of 80, and a chord length of 71, on a minor arc, what is the sagitta?
If I can solve for the sagitta with the two variables (a = arc length, c = chord length), I can solve for radius, diameter, circumference, and more importantly, the angle of the arc.
Thank you for reading, and thank you even more if you can help.
-Dj