I deleted my post after I read yours, second guessed myself and then had a bit of a freak out as I was double checking my maths. I shouldn't have, because I think I'm correct.
My hope was to eliminate the necessity for scribe lines on this particular miter because in my case, it's too dark (I keep a light in my pocket for this task) and too difficult (I had a nasty crash last year that's left me with injuries) for me to crawl on top of my milling machine (in horizontal mode) to see if the cutter is hitting the line.
The problem is that I offset the miters of my seat tube (to the rear) and down tube (downward) so that the edge is tangent to the BB shell. I've been using the top of DT miter length for years, but for the aforementioned reasons, I wanted a way to calculate how far to shift the X-axis of my machine from the centerline of my rotary table when I make this cut.
I came up with the formula :: ST miter offset + [DT miter offset * COS(Miter Angle °)] = x-axis change
Let's say the ST/DT interior angle is 60°, ST miter offset is 0 and DT offset is 10mm. 0 + [10(COS60)] = 5mm. I'd have to slide my x-axis over 5mm from the rotab ctr.
if the ST/DT angle is 30°, ST offset is 0 and DT offset is 10. 0 + [10(COS30)] = 8.66mm
This makes sense because as the miter angle approaches 90° it gets the COS gets closer to 0. At 90°, the DT miter offset has zero effect on the ST miter with 0 as the multiplier. As the miter angle approaches 0° (if that were physically possible) the COS gets closer to 1. At 0°, the x-axis offset would be exactly the DT miter offset because the multiplier is 1
The ST miter offset just gets added to the product of the DT miter offset and the COS of the angle because the ST is the y-axis of the machine. Miter offset is perpendicular to that.
The drawing doesn't provide any answers, but it's a real world example of what I'm trying to get to here.
In this case it's 8 + [3(COS42.9)] = 10.198. In order to cut this without using a scribe line, I'd have to move my x-axis 10.2mm from the center of my rotab.
I hope I've described this better than I did the first time and thanks for taking a look at it.