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Deceiving Simple Geometry Question

  1. Jan 31, 2009 #1

    Here's a simple looking geometry question, but I can't seem to solve it.
    But according to scale models, there is a unique answer for BC.

    Equations with Pythagoras' theorem or cosine rule always seems to end up in an illegible pile of mess. :yuck:

    Does anyone has any idea how to go about solving the question?
  2. jcsd
  3. Jan 31, 2009 #2
    You have 7 unknown angles and there are 7 linear independent equations relating them, so the solution is unique. You can use the angles and trigonometry to find BC.
  4. Jan 31, 2009 #3
    Thanks for pointing out that info.

    But isn't there another way to solve this question rather than to solve a 7 variable simultaneous equation? Most variables are not linear combination of each other too, so I doubt the 7 equations are practically reducible.
  5. Jan 31, 2009 #4
    I was able to find a solution using the Law of Sines on triangle AYX, namely on angles AYX and YAX

    nevermind, i drew the picture incorrectly.
    Last edited: Jan 31, 2009
  6. Jan 31, 2009 #5
    In case anyone wants to check, the answer should be around 3.6 using a scale model.

    By using a software to digest some of the equations i threw in, the answer comes out to approximately 3.580181.

    But of course, the equations are too long for someone to solve by hand. I think someone must have a better method than me. :smile:
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