Arch angle needed. Have, radius, width, rise.

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I use auto cad everyday, all day. I am trying to create a excel spreadsheet, where you can type in given information and receive missing information, rather than drawing out the arch.

For example, 35.75" wide x 47.75" over all height and a leg height of 41.75". This would be an arch.

With the given information, the rise is 6", I can do the math and get the radius, radius is 29.625.

Using autocad, I get an "angle" at the top of the leg of 27 degrees. I am trying to figure out the formula needed to get the 27 degrees

Tried to post a picture but I am to new to do so.

Although it's fine using autocad to do this, I personally would like to know the formula.

And for this life of me I cannot, and I'm sure it's simple enough

Thanks for any and all help