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    trach171's Avatar
    trach171 Posts: 2, Reputation: 1
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    #1

    Nov 14, 2009, 04:53 PM
    Bearings and trigonometry?
    Three towns A, B and C are connected by straight roads. B is due west of A, C is due south of B and the bearing of C from A is 220 degrees. If the distance from A to B is 300 km:

    a) find the distance from A to C

    b) find the bearing from A to C
    jmjoseph's Avatar
    jmjoseph Posts: 2,727, Reputation: 1244
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    #2

    Nov 14, 2009, 05:15 PM
    Based on what you have given, the distance between A and C is 466.7 km, and the bearing from A to C is 220 deg. The bearing from C to A is the reciprocal, 40 deg.

    (Edited)
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Nov 14, 2009, 09:31 PM

    Sorry, but the distance is not good.

    The easiest way to do it is by having a sketch in front of you.

    Name: Test.png Views: 670 Size: 1.8 KB

    You can find angle BAC by having 270 - 220 = 50 degrees
    Using cos, you know that



    Solving for AC will give you 466.7 m.

    Then, the bearing is indeed 40 degrees
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #4

    Nov 16, 2009, 01:27 AM

    Quote Originally Posted by jmjoseph
    I used the diagonal of a 300km x 300km square, and I was obviously wrong. OOPS. I mis-read something. Thanks. Unk!
    It's OK, it might have happened to anybody including myself :)
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