Math Help - Find height of segment given radius and area

1. Find height of segment given radius and area

I have R and I have A how do I solve for theta? From there I can figure out h.

Or is there another formula I could use to find h if I only have the Area and the radius?

2. First: This is a double posting which is against forum rules.
Second: You did not make clear that A is the area of the shaded area in the diagram.
Now I am prepared to be proven wrong in what follows.
It seems to me that your question has no unique solution.
As the circular radius increases and the angle $\theta$ decreases the area of the segment could remain constant.
Therefore, you need to know a third constant.

3. Found own answer

Thanks for trying, I have been fighting with this for awhile, but I found the answer.

You can use Newton's Method to solve for theta - sin(theta).

BTW the diagram is from the website you sent me to so I didn't think that I would have to explain it.
Sorry about the double post I was desperate to find the answer.

4. Originally Posted by lhenderson

I have R and I have A how do I solve for theta? From there I can figure out h.

Or is there another formula I could use to find h if I only have the Area and the radius?

Try this:
sin theta/2=a/2R find the angle
Then, r=R costheta/2
h=R-r