I'm not sure if this is the place to post this question, so please redirect me otherwise?

I'm having trouble with some trigonometry, or geometry and need to calculate the curves necessary to join a sloped edge to an arch (which is a semicircle).

If you look at the pictures below, the first picture is the arch I need to attach the sloped edge to.  If I take side view of this, it will look like the second picture from the left, with the green section showing the top sloped edge which needs to attach (only at the edges) to the semicircle (arch). 

 If I laid out the material flat on the ground, it would look like the third picture.  The sides of the material taper inwards, and the top would have a curve which should be the same arc length as the edge I want to attach it to (the semi-circle arch).

I've tried to take a few directions with this as shown below.  

One was to work out the height of the arch on the piece attaching to the original arch and then find the chord length (which is proving to be impossible as I don't have the radius of the circle my new arch will belong to). 

Would someone mind taking a look at this and maybe providing a hint on how I could go about this.  

If it requires some special software, then could you suggest what that software might be.  Otherwise, the below couldn't be impossible, but I just can't work it out.

Thanks