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March 29, 2017

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On a map, Town A is 8 km due south of Town B, Town C is 9 km from Town A, and Town C is 3 km from Town B (see figure below). Find the bearing from Town A to Town C and the bearing from Town B to Town C.

  • geometry - ,

    Hello, there is no figure but I shall try my best to figure it out.

    I think this is probably a triangle.

    B
    | C
    | /
    | /
    A

    AB= 8
    AC=9
    BC=3


    A is 9 km SW of C and B is 3 km NW of C. I hope this helps.

  • geometry - ,

    Thank you a ton!!

  • geometry - ,

    No problem!

  • geometry - ,

    To find the actual bearings, find the angles A,B,C, using the law of cosines. For example,

    BC2 = AB2 + AC2 - 2*AB*AC*cosA

    9 = 64 + 81 - 144cosA
    cosA = 136/144
    A = 19º

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