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25 November, 08:55

A tree needs to be staked down before a storm. If the ropes can be tied on the tree trunk 8 feet above the ground and the staked rope should make a 30 degree angle with the ground, how far, to the nearest tenth, from the base of the tree should each rope be staked?

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  1. 25 November, 09:00
    0
    divide the height * 8 feet) by the tangent of the opposite angle (30 degrees)

    8 / tan (30) = 13.856

    rounded to nearest tenth would be 13.9 feet
  2. 25 November, 09:13
    0
    Refer to the diagram shown.

    Let x = the distance from the base of three to where the rope is tied.

    By definition,

    tan 30° = 8/x

    0.5774 = 8/x

    Multiply each side by x.

    0.5774x = 8

    Divide each side by 0.5774

    x = 13.855 ft

    Answer: 13.9 ft (nearest tenth)
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