Yes, that expression will give you a reasonable approximation for field of view as long as you are not too close to the subject. The factors that I mentioned above are usually only significant near close focus. For a wide angle lens, 10 feet is likely close enough to infinity (hyperfocal distance for a 10 mm @ f/4 is about 1.5 m) that you can ignore magnification and focal length change when focusing. Note that lens manufacuturers usually quote angular FOV for the diagonal, not the frame width.

Your original question mentioned 1 foot, 5 feet, etc. distances. Predictions at close distance may not be as accurate depending on lens focal length and magnification. For example, my 200 mm Micro provides 1:1 magnification at close focus of just under 0.5 m. This magnification factor by itself would cut the FOV about in half. However, focal length of the 200 Micro is actually about 104 mm at close focus, almost completely canceling the effect of magnification on the FOV. My 105 mm f/2.5 AIS focuses by extension so the focal length does not change. Since at close focus of about 1 m its magnification is about 1:7, the angular FOV is reduced about 14% from that at infinity.