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Math Help - Parallelogram Angle Solving

  1. #1
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    Parallelogram Angle Solving

    Basically just find this angle,


    I used the sine rule and got something like 50.8...etc, And when I rounded it off I got 51.
    But I dont think its right, Anyone help, I think the red 29 that I've indicated is right because its a parallelogram but if its not then I know I went wrong, Any help on how to solve this.
    Thanks

    edit: calculated again, I think the right answer was 50*51
    Last edited by ZettaDigit; March 31st 2010 at 02:46 PM.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by ZettaDigit View Post
    Basically just find this angle,


    I used the sin rule and got something like 50.8...etc, And when I rounded it off I got 51.
    But I dont think its right, Anyone help, I think the red 29 that I've indicated is right because its a parallelogram but if its not then I know I went wrong, Any help on how to solve this.
    Thanks
    Hi ZettaDigit,

    Why don't you think it's right? You're drawing is not drawn to scale, but, other than that, it looks fine.

    Lean your parallelogram the other way and the measures make sense.
    Attached Thumbnails Attached Thumbnails Parallelogram Angle Solving-1.jpg  
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  3. #3
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    Hello, ZettaDigit!

    The problem is the dreaded "ambiguous case".
    There are two solutions.


    Find angle x.
    Code:
              C o - - - - - - - - - - - o D
                 \  *                    \
                  \  x  *                 \
                   \        *              \
                    \ 5         *           \
                     \              *        \
                      \                 *     \
                       \               29  *  \
                      A o - - - - - - - - - - - o B
                                    8

    Law of Sines: . \frac{\sin x}{8} \:=\:\frac{\sin29^o}{5} \quad\Rightarrow\quad \sin x \:=\:\frac{8\sin29^o}{5} \:=\: 0.775695392

    Therefore: . x \:\approx\:\boxed{50.9^o}



    But inverse sine can have more than one value.

    Hence: . x \:=\:180^o - 50.9^o \;=\;\boxed{129.1^o}

    And the parallelogram looks like this:


    Code:
              C * - - - - - - - - - - - - - - - - - - - * D
               /    *                                  /
              / 129.1  *                             /
             /              *                        /
          5 /                   *                   /
           /                        *              /
          /                             *         /
         /                             29  *    /
      A * - - - - - - - - - - - - - - - - - - - * B
                            8
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