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Math Help - Apothem

  1. #1
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    Apothem

    I understand how to find the apothem, but i dont know what to do with it afterwards.

    If the apothem of a regualr pentagon is 10.8 what would be the radius of the circumscribed circle?

    my book doesnt say much on solving this...

    and how would you find length and perimeter?
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  2. #2
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    The apothem is the distance from the center to the midpoint of a side of the pentagon. So, if we draw that line and one to the corner of the pentagon(which is the radius of the circle) we get a right triangle.

    The angle of this right triangle is 36 degrees = Pi/5 radians. See why?.

    radius=10.8sec(\frac{\pi}{5})=\frac{10.8}{cos(\fra  c{\pi}{5})}

    The length of a side of the pentagon would be 21.6tan(36)

    We could also get it from the radius we found by using sine: 21.6sec(36)sin(36)
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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  3. #3
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    i see where you got 36. [ 360 divided by 10 ]
    where did 5 come from?
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  4. #4
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    Which 5?. The Pi/5?. That is just the radian equivalent of 36 degrees. Whatever you want to use.

    The 5.4 came from making a mistake. I fix. That should be 21.6
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  5. #5
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    i dont understand
    ...how do you find the radius?
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  6. #6
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    I just showed you. It's just a little trig. Look at the triangle.
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  7. #7
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    i understand how you found the length and perimeter i dont understand the radius. the formula is confusing
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  8. #8
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    Quote Originally Posted by galactus View Post
    Which 5?. The Pi/5?. That is just the radian equivalent of 36 degrees. Whatever you want to use.

    The 5.4 came from making a mistake. I fix. That should be 21.6

    oooohh ok i see now. i just read the mistake.
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