NavList:

Robin Stuart you wrote:  "and assuming a gaussian error distribution with standard deviation σ as above, the probability that the thin triangle encloses the observer's true position is 34.7%. I attach a spreadsheet that computes the quantities described here."

That and all that precedes it is a great answer, Robin.  It saves me asking the question I was going to ask.  It also confirms what I was sure I’d read somewhere on the probability of your true position being inside the cocked hat. 

Will the spreadsheet you posted work for anyone altering the azimuths and intercepts?  I have in mind setting it up with three PL 120 degrees apart and then seeing how the probability changes as the lengths of the three intercepts are altered equally.  There must be some reason why a tiny cocked-hat gives you a warm ‘fuzzy’ feeling or is that a different proposition?  DaveP