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{Geometry} Find length of the equilateral triangle

  1. Jul 23, 2015 #1
    1. The problem statement, all variables and given/known data
    http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers



    2. Relevant equations
    The radius of the circle and properties of the equilateral triangle

    3. The attempt at a solution
    ThetaBig = ThetaSmall = 60

    SideBig * sin(60deg)+SideSmall * sin(60deg) = 2 * radius

    SideSmall = (2 * radius - SideBig * sin(60deg)) / sin(60deg)

    SideSmall = 2 * radius / sin(60deg) - SideBig

    This gave me fraction answer of 64/3 - 16 not in the correct form
     
  2. jcsd
  3. Jul 23, 2015 #2

    DEvens

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    According to the picture this is not the case. The left side is actually a little bit less than 2 * radius, because the smaller triangle does not touch the circle at the bottom middle.
     
  4. Jul 23, 2015 #3
    Picture is human error on my part with bad paint skills
     
  5. Jul 23, 2015 #4

    DEvens

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    I don't think I made myself clear. You have worked out the combined height of the two triangles, and this is slightly less than the diameter of the circle.
     
  6. Jul 23, 2015 #5

    SteamKing

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    Since we are dealing with equilateral triangles, it's not clear what "Side Big" and "Side Small" are.
     
  7. Jul 23, 2015 #6

    DEvens

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    Look at the picture. There is a big triangle and a small triangle.
     
  8. Jul 23, 2015 #7
    Side big is meant to be the side of the bigger triangle which is known as 16. The small side is the one I'm trying to find expressed as Asqrt(B)-C where they are all integers.
     
  9. Jul 23, 2015 #8
    Ah yes I ended up using law of cosines and got the correct answer thank you for the hint.
     
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