I Need Equivalent Formulas to solve for various elements of an arc - width, height, and radius

[dirtfarmerjay]

Hi, Smart People! I'm out of my element. I am a YouTube Creator (dirtfarmerjay) that has produced a video showing how to create basic arcs (a slice off the "edge" of the a circle). I'd like to show how to calculate various measurements, depending on known information. In the equation I have, we are solving for the radius. But I'd like other versions/equivalents of this formula, so we can solve for endpoint distance of the arc, or the height of the arc.

In this equation, R=radius, A=desired width of the arc, and B=height of the arc (distance from the center of the arc baseline to the arc center). As I said before, the formula I have solves for the radius. I've attached a picture of the equation.

Can someone kindly provide the other two equivalent equations that solve for A and B?

As that famous mathematician, Clint Eastwood/Dirty Harry, once said, "A man has got to know his limitations." I know solving this is beyond mine. I appreciate your help!

"DirtFarmer" Jay

 

[Dr.Peterson]

Can someone kindly provide the other two equivalent equations that solve for A and B?

First, your A is called the chord, and your B is called the sagitta, or height.

Your equation is correct; this gives an equivalent equation: https://en.wikipedia.org/wiki/Circular_segment#Radius_and_central_angle

Taking a link from there, you can find that equation solved for the chord length or sagitta here, using different variable names: https://en.wikipedia.org/wiki/Sagitta_(geometry)

 

[dirtfarmerjay]

Dr. Peterson, YOU ROCK. Thanks for your immediate and authoritative response. When we produce this episode, may I give you credit for sending me in the right direction? Regards, DFJ