Angle = arctan (Difference / Size picture * Size recording / (Focal length * (1 + Magnification))
= 'distance from rear principal point to recording
plane' / 'distance from front principal point to subject (object)'
(can be assumed zero in the case when one takes no macro exposures).
Remark: make sure no barrel of pincushion distortion is
present in the picture (SLR cameras tend to have less of this, because
of proper optics).