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March 28, 2017

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A ship sails 5 km from a port A on a bearing of 85 degrees and then 6 km on a bearing of 50 degrees. Calculate the distance and bearing from A.

  • Geometry - ,

    calculate the horizontal and vertical replacements of each trip
    first trip:
    x/5 = cos85 , x = 5cos85
    y/5 = sin85 , y = 5sin85

    2nd trip:
    x/6 = cos50 , x = 6cos50
    y/6 = sin50 , y = 6sin50

    total horizontal displacement
    = 5cos85 + 6cos50 = appr 4.2925
    total vertical displacement
    = 5sin85 + 6sin50 = appr 9.5772

    now use Pythagoras ... to get

    √(4.2925^2 + 9.5772) = 40.4952

    or

    just add the vectors
    ((5cos85,5sin50) + (6cos50,6sin50) and take their magnitude.

    (the actual calculations are the same as above)

  • Geometry - ,

    THANK YOU

  • Geometry - ,

    Are we worried whether we use compass headings where North = 0 degrees, rather than East, and angles are measured clockwise?

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