"based on this information can work out the radar beam width in degrees."
I'm not sure if you can work out the beamwidth with antenna diameter alone. Mr Trammell is probably assuming that the antenna is an old parabolic style antenna and not like a modern flatplate antennae(?). Even so, on the older parabolic systems, you could have a variable beamwidth. If my memory hasn't failed me, I recall some commercial airliner radar systems had a "pencil" beam for ground mapping (as well as the wider, weather mapping beams). Can't remember how the different beams were generated though.
For interest, the antenna width of a flat plate 737NG antenna is 23" wide with a beam width of 5.4 degrees (Does this match his formula?).
Rgds.
NSEU