Stats for a full-frame 35mm camera, taken from lens manufacturers' spec sheets.

• 50mm = 46 degrees
• 70mm = 34 degrees
• 135mm = 18 degrees
• 200mm = 12 degrees

Now, those are presumably across a circular diameter (ie. the diagonal of a frame).

For a 3m wide backdrop, your hypotenuse in 3:2 aspect ratio is sqrt(13), or 3.6m.

Now use some trig to convert those angles into 3.6m.

Working

For a 50mm lens:

• theta = 23 degrees
• Opposite = 180cm

tan(23 degrees) = 180 / working distance

0.42 = 180 / working distance

1/0.42 = working distance / 180

180/0.42 = working distance

working distance = 428cm?

I don't think this is correct...