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Math Help - Bearing word problems help

  1. #1
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    Bearing word problems help

    They are driving me crazy. Please help..

    1.) A plane took off on a runway having a bearing of 75 degrees. After flying for 1.5 miles, the pilot turned 90degrees and headed toward northwest. After the plane goes 3 miles in this direction, what bearing should the control tower use to locate the aircraft?


    2.) Two ships leave a pier at the same time. Ship A sails in the direction of 55degrees at 20 knots while ship b sails in the direction of 145 at 25 knots. Determine after traveling 3 hrs the distance between the ships. What is the bearing of ship A from ship B?

    3.) A ship leaves a port and sails for 3 hrs on a course N78degrees E at 12 knots. Then the ship changes its course to 168degrees and sails for 5 hours at 10 knots. After 8 hours, how far is the ship from the port? Determine the bearing of the ship from the port.


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    Please help.. Thank you very much!
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  2. #2
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    The first step is to draw a diagram (assuming you aren't using vectors yet). I have drawn it for the first one.
    Bearing word problems help-dtfd.jpg

    Then just start filling in the things you can deduce from the picture.
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  3. #3
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    Hello, fayeorwhatsoever!

    3) A ship leaves a port and sails for 3 hrs on a course N78E at 12 knots.
    Then the ship changes its course to 168 and sails for 5 hours at 10 knots.
    After 8 hours, how far is the ship from the port?
    Determine the bearing of the ship from the port.
    Code:
          N       M
          :       :
          :       :
          :     A o 168
          :      *  * 
          :     * 90 *
          :    *        *
          :78* 36        *  50
          :  *              *
          : *                 *
          :*                    *
        P o                       *
                *                   *
                      *               * 
                            *           * 
                                  *       * 
                                        *   *
                                              o B

    The ship starts at port P. . \angle NPA = 78^o
    It sails 36 nautical miles to A.

    It changes course to \angle MAB = 168^o
    . . and sails 50 nautical miles to B.
    Note that \angle PAB = 90^o.

    Pythagorus: . PB^2 \:=\:36^2 + 50^2 \:=\:3796 \quad\Rightarrow\quad PB \:=\:\sqrt{3796} \:\approx\:61.6

    The ship is about 61.6 nautical miles from the port.



    In right triangle PAB\!:\;\;\tan(P) \:=\:\tfrac{50}{36} \quad\Rightarrow\quad P \:=\:\tan^{-1}\left(\tfrac{50}{36}\right) \:\approx\:54.2^o

    The bearing is: . \angle NPB \;=\;78^o + 54.2^o \;=\;132.2^o

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