Calculate arc Sagitta from radius and arc length

Question

I have an arc, I know the radius of the circle, and I know the angle arc covers so I can calculate its length. eg. arc of angle 180 will have will have length half of perimeter of circle. But what I need is the segitta of the arc. After searching online I found ways to calculate segitta from radius and chord of arc. But since I don't know the chord length either I can't do that.

Answer 1

If $r$ is radius, $\alpha$ is the arc angle, the sagitta $h=r(1-\cos \frac{\alpha}{2})$. Connect the ends of the chord with the center and you get isosceles triangle so the height will also be a median and a bisector.