math

you have an unfortunate brush with the law and you are required to spend some time in the penitentiary. (Naturally you have brought your math 30 course notes with you for a bit of light bedtime reading. You also hope to enlighten your fellow inmates with your mathematical virtuosity.) One day, while exercising in the yard, you observe that one of the watch-towers presents an interesting mathematical problem. The 100 foot vertical tower is erected on the side of a hill that makes a 11 degree angle with the horizontal. Two guy wires are attached to the top of the tower. The guy wires are aligned with the fall-line of the hill and are anchored in the ground 100 feet directly uphill and downhill from the center of the tower base. You wish to calculate the length of each guy wire.

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  1. let the two wires have length
    d for the downhill wire
    u for the uphill wire

    d^2 = (100+100sin11°)^2 + (100cos11°)^2
    d = 154.3

    u^2 = 100^2 + 100^2 - 2(100)(100)cos79°
    u = 127.2

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