A few min spare today - and I could see it from the cosine rule, not needing the sine rule.

So by my estimation it is just under 8.1 miles (my calculator makes it 8.097 - but in reality probably fractionally more because that doesn’t allow for the cars, pedestrians and dogs you may have to dodge en route).

Ha ha ! there are no cars, pedestrians or dogs en-route..........this is winky's valhalla !!!

Your estimation is very close to the correct figure.......this is a nice, but encouraging way of saying it's wrong! But what a bloody good shot !

I didn't use the Cosine Rule, but that doesn't mean your technique is wrong, you might just have had a bit of "finger" wobble putting the numbers into your calculator.

The correct answer is just over 8.1 miles, but it is a very precise fraction that makes it "just over" 8.1

If you post a few more details of your approach, I'll see if I can spot any obvious goofs.

Later today, I will outline the three formulae, that I used in order to derive a very simple, and somewhat satisfying formula for R. I rather suspect that some people might well have written this simple formula down in their school days, along with the FULL Sine Rule and a few other formulae. I didn't, so had to derive it when I first saw this teaser !

Your answer is certainly within a gnat's whisker !!