Stats for a fullframe 35mm camera, taken from lens manufacturers' spec sheets.
 50mm = 46 degrees
 70mm = 34 degrees
 85mm = 28 degrees
 135mm = 18 degrees
 200mm = 12 degrees
Now, those are presumably across a circular diameter (ie. the diagonal of a frame).
Contents
Working in landscape orientation
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.
Cheating: divide your focal length (mm) by 11.76 to get the distance in metres
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?
4.3 metres
My mathematical gut feeling says this is wrong... but it seems about right when I hold the 50mm up to my eye.
70mm lens
theta = 17 degrees working distance = 180 / tan(17) = 180 / 0.306 = 588cm
5.9 metres
85mm lens
Working distance = 180 / 0.249 = 7.23 metres
135mm lens
theta = 9 degrees working distance = 180 / tan(9) = 180 / 0.158 = 1136cm
11.3 metres
200mm lens
theta = 6 degrees working distance = 180 / tan(6) = 180 / 0.105 = 1712cm
17.1 metres
Working in portrait orientation
For a 3m wide backdrop, your hypotenuse in 2:3 aspect ratio is sqrt(29.25), or 5.4m.
Now use some trig to convert those angles into 5.4m.
Cheating: divide your focal length (mm) by 7.87 to get the distance in metres
For a 50mm lens
theta = 23 degrees working distance = 270 / tan(23) = 270 / 0.424 = 636cm
6.3 metres
70mm lens
theta = 17 degrees working distance = 270 / tan(17) = 270 / 0.306 = 883cm
8.8 metres
85mm lens
Working distance = 270 / 0.249 = 10.8 metres
135mm lens
theta = 9 degrees working distance = 270 / tan(9) = 270 / 0.158 = 1704cm
17 metres
200mm lens
theta = 6 degrees working distance = 270 / tan(6) = 270 / 0.105 = 2568cm
25.6 metres
Portrait mode with 2m fixed height subject
 2m high
 1.33m wide
2.4m diagonal
 1.2m for rightangle triangle (120cm)
Cheating: divide your focal length (mm) by 17.71 to get the distance in metres
50mm lens
 theta = 23 degrees
 working distance = 120 / tan(23)
2.82 metres
70mm lens
Working distance = 120 / 0.306 = 3.92 metres
85mm lens
Working distance = 120 / 0.249 = 4.82 metres
135mm lens
Working distance = 120 / 0.158 = 7.59 metres
200mm lens
Working distance = 120 / 0.105 = 11.4 metres
In a table

3m landscape max. 
2m portrait max. 
2m fixedheight subject 
50mm 
4.3 
6.3 
2.8 
70mm 
5.9 
8.8 
3.9 
85mm 
7.2 
10.8 
4.8 
135mm 
11.3 
17.0 
7.6 
200mm 
17.1 
25.6 
11.4 
Diagrams
Working room for subject
Assuming a 2m high subject, and a 3m x 3m backdrop, we have a certain amount of room to play with.
Using the figures from the table, and assuming portrait mode:
 Photographer can move back as far away as the second column ("2m portrait max.")
 Subject must be further from photographer than the distance in the third column (aka. "clipping distance")
 Subject could be right up against the backdrop, in theory
$col3  $col2 = playspace

2m portrait max. 
Clipping distance 
Playspace in metres 
50mm 
6.3 
2.8 
3.5 
70mm 
8.8 
3.9 
4.9 
85mm 
10.8 
4.8 
6.0 
135mm 
17.0 
7.6 
9.4 
200mm 
25.6 
11.4 
14.2 