Arc length of a sine wave kinda

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I find myself trying to work out a formula to help in speeding up a task i do on a daily basis, but it seems to be beyond my education.

I'm trying to work out the length of a sort of sine wave that consists of 2 arcs of the same length and a straight line joining the two:

enter image description here

I currently draw this in CAD and tweek the "A" & "B" values to get the length of this black line to match a pre calculated length. However, I want to calculate values "A" & "B" from the line length that is pre calculated.

For example: "A" = 60mm "B" = 140mm "C" = 21mm

What would the formula be to find the length of the black Sine wave length?

In CAD this comes to 178.249mm

But I want to calculate "A" & "B" in excel so a formula is needed.

Thanks in advance.