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Math Help - Diagram and Trig/Pre-Calc prob... really confusing...

  1. #1
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    Diagram and Trig/Pre-Calc prob... really confusing...

    At a criminal trial, the witness gave the following testimony: "the defendant was 20 ft from the victim. I was 50 ft from the defendant and 75 ft from the victim when the shooting occurred, I saw the whole thing."
    a) Use the law of cosines to show that the testimony has errors.
    b) How else could you know that the testimony has errors?

    Thanks!!!
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  2. #2
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    Re: Diagram and Trig/Pre-Calc prob... really confusing...

    Hello, aioria1995!

    Did you make a sketch?


    At a criminal trial, the witness gave the following testimony:
    "The defendant was 20 ft from the victim.
    I was 50 ft from the defendant and 75 ft from the victim when the shooting occurred."

    a) Use the Law of Cosines to show that the testimony has errors.
    Code:
                  20
        D o  *  *  *  *  *  o V
           *              *
            *           *
          50 *        * 75
              *     *
               *  *
                o
                W
    75^2 \:=\:20^2 + 50^2 - 2(20)(50)\cos D \quad\Rightarrow\quad 5625 \:=\:2900 - 2000\cos D

    2000\cos D \:=\:-2725 \quad\Rightarrow\quad \cos D \:=\:-\frac{2725}{2000} \:=\:-1.3625

    But \cos D must be betweeen \text{-}1 and +1

    The witness' description is impossible.




    b) How else could you know that the testimony has errors?
    Lengths of 20, 50, and 75 cannot form a triangle.
    Code:
                  *       *
             20 *             *    50
              *                   *
            *                         *
          *   *   *   *   *   *   *   *   *
                        75
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