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    Mike isaac's Avatar
    Mike isaac Posts: 2, Reputation: 1
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    #1

    May 24, 2012, 10:40 AM
    Bearing
    A boat soils 4km on a bearing 038degree and then 5km on a bearing of 067degree.(a)how far is the boat from its starting point? (b)calculate the bearing of the boat from its starting point?
    zenton's Avatar
    zenton Posts: 6, Reputation: 1
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    #2

    Jun 10, 2012, 02:16 AM
    Bearing from the point after 4km to the starting point is 180-038=142degree.
    So if you draw the 4km line and 5km lines on a piece of paper, there are 3 angles around that point 4km from the starting point, with 142 and 67 degree.
    Find the last angle which is 360-142-67=151 degree.

    a)
    Using the cosine rule,
    the distance=√(4x4+5x5-2x4x5xcos151)
    =√75.98479
    =8.71693
    =8.72 (3s.f.)

    b)
    Using Sin rule,
    sin151 / 8.71693=sinX / 5
    sinX=0.27809
    X=016.14624 degrees (5d.p.)

    bearing of the boat from its starting point=016.14624+038
    =054.1 degree

    :D
    Good Luck!

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