Look at an analogue clock: the angle between twelve and one o'clock is 30 degrees. Look closer. The angle between adjacent minute (or second) markings is 6 degrees.
Take out a protractor. Look at the one degree markings. Now imagine one tenth of that. Or, imagine looking at a point object 100 metres away, then look at an object 1/10th of a degree away, or just 17.5 cm away (about seven inches for the metrically-challenged, the length of a football field away).
Now do the trig / arithmetic to figure out how many bits of precision you need.