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Math Help - Triangle - Urgent

  1. #1
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    Exclamation Triangle - Urgent

    In a triangle ABC, X is a point on AC such that AX = 15m, XC = 5m, <AXB = 60 degrees and <ABC = 120 degrees. Find the length of BC.
    Last edited by coatsy; August 2nd 2007 at 02:25 AM.
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  2. #2
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    Hello, coatsy!

    In \Delta ABC,\:X is a point on AC such that:
    . . AX = 15\,m,\,XC = 5\,m,\;\angle AXB = 60^o,\;\angle ABC = 120^o
    Find the length of BC.
    Code:
                  B 
                  *
                 * * *
                *   *   *
               *     *     *
              *       *       *
             *         *         *
            *           *           *
           *         60 * 120        *
          * * * * * * * * * * * * * * * * *
          A      15       X       5       C

    Since \angle AXB = 60^o,\;\angle CXB = 120^o

    \Delta ABC has \angle ABC = 120^o and \angle C
    \Delta CXB has \angle CXB = 120^o and \angle C
    . . Hence: . \Delta ABC \sim \Delta CXB

    We have: . \frac{BC}{20} \,=\,\frac{5}{BC}\quad\Rightarrow\quad BC^2 \,=\,100\quad\Rightarrow\quad\boxed{BC \,=\,10}<br /> <br />

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