pre- cal

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An antenna is on a hill that makes a 5 degree angle with the horizon. The antenna is placed so that it is perpendicular to the horizon. A guy wire extends from the top of the antenna to a point 50 ft downhill from the base of the antenna. If the antenna is 25 ft tall, what is the length of the guy wire.

  • pre- cal -

    As usual, draw a diagram.

    Draw a horizontal line from the base of the wire to the base of the tower. (It will lie underground, but give you a right triangle to work with.)

    If we label
    T = top of tower
    W = base of wire
    B = base of tower
    P = the point below the base of the tower where the horizontal line from B intersects.

    Let u = BP
    v = WP

    u = 50sin5° = 4.36
    v = 50cos5° = 49.81

    wire length = √(v^2+(25+u)^2)
    = √(49.81^2 + 29.36^2)
    = 57.82

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