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Math Help - bearing

  1. #1
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    bearing

    bearing-bearing.png


    kindly answer the bearing... i got the angle at forest island but i dont know how to get the bearing in from forst island to home port..

    the bearing should be South East, but what degrees
    Last edited by mr fantastic; September 6th 2010 at 03:48 AM. Reason: Merged posts.
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  2. #2
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    Hello, aeroflix!

    A fisherman leaves his homeport and heads in the direction N\,70^o\,W.
    He sails 30 miles and reaches Egg Island.

    The next day he sails N\,10^o\,E for 50 miles to Forest Island.

    (b) Find the bearing from Forest Island back to his homeport.

    In my diagram, I omitted the distances (they wouldn't fit).
    I hope you read it.

    Code:
                F
                ♥
          Q    *:
          :   * :*
          :10*  :
          : *   : *   P
          :*    S     :
        E ♥100     *  :
          : *         :
          :70 *     * :
          :     *   70:
          R       *  *:
                    * :
                      ♥ H

    The homeport is H.

    He sails 30 miles to E.
    . . \angle PHE = \angle HER = 70^o,\;HE = 30

    Then he sails 50 miles to F.
    . . \angle QEF = 10^o \quad\Rightarrow\quad \angle FEH = 100^o,\;\; EF = 50



    I assume that part (a) asked for the distance from  F to H.

    . . FH^2 \;=\;30^2 + 50^2 - 2(30)(50)\cos100^o \;=\;3920.944533

    Hence: . FH \;=\;62.61744592 \;\approx\;62.62



    Now we determine \angle FHE.

    . . \cos(\angle FHE) \;=\;\dfrac{30^2 + 62.62^2 - 50^2}{2(30)(62.62)} \;=\; 0.61781763

    Hence: . \angle FHE \;=\;52.84305918^o \;\approx\;51.8^o

    Then:. . \angle PHF \;=\;70^o - 51.8^o \;=\;18.2^o

    Note that: . \angle SFH = \angle PHF


    Therefore, the bearing is: . S\,18.2^o\,E

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  3. #3
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    thanks soroban.. now i realize that there are some same angles
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