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Challenging problem corrrection no sine and no cosine law

  1. May 7, 2009 #1
    sorry about the mistake in my last post. I miswrote the bottom vertex of the equilateral triangle.

    Let me re-state the problem correctly

    This is the 3rd and final question I post from the book, The Unsolvable and the Solvable.

    It is NOT a homework question. This is something for everyone to try out for interest.

    Consider an isoceles triangle ABC and an equilateral triangle BCF which share the side BC as shown below. Please ignore the dotted lines.

    ...........................A


    ...................D
    ......................................E

    .............B_________________C



    ...........................F

    D is a point on side AB and E is a point on side AC.

    angle DAE=20 degrees
    angle DEA=20 degrees
    angle EDC=10 degrees
    angle ECD=10 degrees
    angle DBC=80 degrees
    angle DCB=70 degrees
    angle BDC=30 degrees

    WITHOUT using the sine and cosine law, determine angle EFC.
     
  2. jcsd
  3. May 9, 2009 #2
    Label the following unknown angles:

    a = BDF b = FDC c = DEF d = FEC e = BFD f = DFE g = EFC

    Then, write 7 different equations involving them.

    For example, a + e + 140 = 180.

    Once you have 7 equations with 7 unknowns, it can be solved. Though, it is messy. If you know linear algebra, I would use matrices to solve the system.
     
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