how to find the maximum height perpendicular to arc without knowing radius of the arc I am doing the curvature correction of the object boundary, I need to calcluate the maximum height perpendicular to the arc shown in the figure.
I know the chord length and arc length, But i don't know the radius of the arc.
I would like to know how to find out the maximum height perpendicular to the the arc if we have only two parameters like W and A. 
Please help me to solve this problem. 
Thanks in advance. 

 A: If $\theta$ is half the center angle (in radians) subtended by the arc ($0\le\theta\le\pi$), and $R$ the arc radius, then we have:
$$
A=2R\theta,\quad W=2R\sin\theta,\quad
\hbox{and}\quad
H=R(1-\cos\theta).
$$
Dividing the second equation by the first one gets
$$
{\sin\theta\over\theta}={W\over A},
\quad\hbox{that is:}\quad
\mathop{\rm{sinc}}\theta={W\over A}.
$$
This equation has a unique solution $\theta\in(0,\pi)$, if $0<W/A<1$ (as it should be), but there is no commonly defined name for the inverse of the sinc function.
The value of $\theta$ must then usually be found by some numerical method.
Once you find $\theta$, just plug it into the first equation to get $R$ and then use the third equation to find $H$.
A: Here's the simple solution you're looking for, but it's only an approximation, plus or minus 2 or 3%.
s=sagitta (or height), a=arc length, c=chord length
s = 0.42 * √( a^2 - c^2 )
c = √( a^2 - (s/0.42)^2 )
a = √( c^2 + (s/0.42)^2 )
If the arc is more like a full semi-circle (where radius=sagitta), then the constant will be a little closer to 0.4127. If the arc is more flat (very large radius), then the constant will be closer to 0.43. But these are minor differences for an approximation.
