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It must come up in all sorts of practical situations where people need a right angle. Groundsmen doing sports pitch marking is one I have experience of... we used to use a long tape measure and do a sort of massive protractors exercise scoring curves in the grass with a peg and then running...

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Yes. My mistake was trying to draw it out on a piece of paper with the hole directly above the tee (on the basis that a "straight" rather than hooked shot would go from tee to green) which obviously then doesn't work...!!!

I am familiar with Pythag. I was struggling to accept that a right-angled triangle could be assumed but have got there now...

How is 290 worked out...?

When playing golf, I hook my first shot, which lands 200 yards due north of the tee and 210 yards due west of the hole. How far is it from hole to tee?