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    Re: Medieval Navigation Problem
    From: Frank Reed
    Date: 2019 Nov 26, 10:42 -0800

    Want to know the actual distance and angles and all that? Then you do as I said earlier and seek out one of the early derivations of the law of reflection based on least time. The simplest trick is to look at the target "in the mirror". So flip the barn over to the other side of the river to its exact mirror image. That image is 200 yards east of the river. The house remains 400 yards west of the river and the north-south distance (parallel to the river/mirror) is still 800 yards. So the distance N/S is 800, the distance E/W (to the mirror image) is 600. Divide both of those numbers by 200, and you get 4 and 3... Therefore, you have a 3-4-5 triangle so the straight line distance from the house to the mirror image of the barn is 5 units or 1000 yards. 

    Frank Reed


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