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A wire is stretched from the ground to the top of an antenna tower. The wire is 20 feet long. The height of the tower is 4 feet greater than the distance from the tower's base to the end of the wire. Find the height of the tower.

20 ft.= w
x.4 = height of tower

something like this?

  • math -

    I must assume that the wire's base is attached at some distance from the bottom of the tower, like a "guy-wire".
    (Broken Link Removed)

    Let the tower's height be H and the length of the wire be L = 20.

    Use the Pythagorean theorem:

    20^2 = H^2 + (H-4)^2

    and solve for H.

    400 = 2 H^2 -8H + 16
    H^2 -4H -192
    (H-16)(H+12) = 0
    Take the positive root, H = 16 feet.
    The tower's base is sqrt (20^2 - 16^2) = 12 feet from where the cable touches the ground.

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