Arc central angle from Arc width and height

Question

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.

Answer 1

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.