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Math Help - Urgent Trigonometry help needed

  1. #1
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    Urgent Trigonometry help needed

    Radar stations A and B are on an east-west line, 3.7km apart. Station A detects a plane at C with a bearing of 61 degrees. Station B also detects the plan with a bearing of 331 degrees. Find the distance from A to C.

    I have drawn many different diagrams but none seem to be the right one. Could someone please help me?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello. lax600!

    Are you sure you understand bearings?
    They are measured clockwise from due North.


    Radar stations A and B are on an east-west line, 3.7 km apart.
    Station A detects a plane at C with a bearing of 61.
    Station B also detects the plane with a bearing of 331.
    Find the distance from A to C.
    Try it with this diagram . . .
    Code:
                        C
                        *
        P             *  *      Q
        :           *     *     :
        :         *        *    :
        :       *           *29:
        :     *              *  :
        :61*                 * :
        : * 29            61 *:
      A * - - - - - - - - - - - * B
                  3.7

    We are given: . \angle PAC = 61^o
    . . Hence: . \angle CAB = 29^o

    We see that: . \angle QBC = 29^o
    . . Hence: . \angle CBA = 61^o

    Then: . \angle C \:=\:180^o - 29^o - 61^o \:=\:90^o
    . . \Delta ABC is a right triangle.

    We have: . \sin 61^o \:=\:\frac{AC}{3.7}

    Therefore: . AC \:=\:3.7\sin61^o \:=\:3.236092916 km.

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