Geometry

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

  • Geometry -

    Just set it up like a right triangle problem.

    In fact this problem is a special triangle problem dealing with 30,60,90 degree triangles.

    I recommend drawing a picture with these dimensions:

    *Your x leg is 15ft
    *y leg is the height of the statue (what you want to find), for now represent this as y
    *Your angle of 60 degrees will be the one near the woman's eyes
    *The 30 degree angle will be the one near the top of the statue when you draw the triangle

    Now recall the special relationships with all the angles and the sides

    *the side across from the 30 degree angle = x
    *the side across from the 60 degree angle = x√3

    In this situation you have here you can see that the side across from the 30 degree angle is 15ft so that means:

    15ft = x

    This means that 15√3 = x√3, the side across from the 60 degree angle so this is the part of the height of the statue

    Now, I say part of the height because the woman is viewing the statue at a height of 5 feet so you need to add on that 5 feet to the statue's height as well.

    You should end up with 15√3 + 5 ft, if you need the decimal approximate you can type it into your calculator to find out.

  • Geometry -

    Let h be the height of the statue which lies above the woman's height of 5 ft

    h/15 = tan60°
    h = 15tan60
    = 15√3

    so the height of the statue is 15√3 + 5

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