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Math Help - Need help finding an angle in degrees

  1. #1
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    Need help finding an angle in degrees

    A map suggests that Atlanta is 731 mi in a direction of 4.90 north of east from Dallas. The same map shows that Chicago is 562 miles in a direction of 21.0 west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.
    magnitude

    Now I've drawn this out and I get distance between dallas/chicago = 774 miles.

    Now as far as the angles inside the triangle I used the law of sines.

    sin(a)/A = sin(b)/B = sin(c)/C I know the answer is between 41.2 and 48.6 but I think I made a calculation error somewhere because I keep slightly getting the wrong answer.

    Ive got less than one hour.
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  2. #2
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    Hello, thedoge!

    Your diagram must be off . . . We use the Law of Cosines.


    A map suggests that Atlanta is 731 mi in a direction of 4.90 north of east from Dallas.
    The same map shows that Chicago is 562 miles in a direction of 21.0 west of north from Atlanta.
    Find the displacement from Dallas to Chicago.
    Code:
                        C *             :
                            *           :
                              * 562     :
                                *       :
                                  * 21 :
                                    *   :
                                  69 * :
                          - - - - - - - * A
                            4.9  *
                      731   *
                      *
                * 4.9
        D * - - - - - - - - - - - -

    We have \Delta CAD with: . \angle CAD = 73.9^o,\:AC = 562,\:AD = 731

    Law of Cosines: . DC^2\:=\:562^2 + 731^2 - 2(562)(731)\cos73.9^o \:=\:622,351.079

    Therefore: . DC \;\approx\;788.89 miles.

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  3. #3
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    Too late to help on my homework, but you still helped me to understand the problem. Thank you.

    I had figured my initial distance was incorrect, but it was graded correctly.
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