Assuming your not using map contact updates though, if you are you can just mark it, of course if you have map contact updates enabled you can get all your mesurments from the chart if you wanted.
I will say this though you have a fairly wide margin for error with aob, less so with range and speed. Of course the further the target the smaller the margin for error becomes
As for taking the shot, its more important to position yourself in a good position to take the shot, then trying to quickly get the shot off. Idealy you calculate the speed and just before shooting you update the range and AoB. The TDC will update the Aob based on bearing information from the sighting insturment (but it always assumes the target is continuing on the exact same course, and your own ship's motion can throw it off). It wont update the range though.
If your trying to manualy plot out the ship (no contact update), you need to get the range and bearing, start the stopwatch, plot it out then take the second reading of range and bearing at 3 minutes 15 seconds (thats 3.25 minutes). and plot it out. with those 2 points you now know its course, speed, and position, and using the protractor you can get a pretty exact AoB reading.
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