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A 5 foot tall woman stands 15 ft from a statue. She must look up at an angle of 60° to see the top of the statue. How tall is the statue?

  • Geometry - ,

    It's easier if you drew the figure, but it's hard to draw figures here so I'll just describe it. :3
    Note that the woman is 15 ft from the statue, and she looks up at an angle of 60° in order to see the top of statue. From here we can actually form a right triangle, with base 15 ft, the height unknown, and 60° angle between the hypotenuse and base.
    Let h = height of triangle, which is also the height of statue minus the height of woman. Thus,
    tan 60° = h / 15
    h = 15 * tan 60°
    h = 15*sqrt(3)

    Therefore the total height of statue is h plus the height of woman, which is 15*sqrt(3) + 5 ft, or 30.98 ft

    Hope this helps~ :3

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