Math

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"A ship leaves port on a bearing of 34.0 degrees and travels 10.4 mi. The ship then turns due east and travels 4.6 mi. How far is the ship from port, and what is its bearing from port?"

I would like to know how the actual steps in finding the answer please!

  • Math -

    just start drawing your lines, and figure out how far each leg of the trip takes the ship. Start at (0,0)

    go 10.4 mi at N34°E puts you at

    (10.4*sin34°,10.4*cos34°) = (5.82,8.62)

    Now go E for 4.6, and that adds (4.6,0) to the displacement. Now you are at

    (10.42,8.62)

    The new bearing θ is given by

    tanθ = 10.42/8.62 = 1.2088
    θ = 50.4°
    distance is sqrt(182.88) = 13.52

    or, 13.52mi at N50.4°E

  • Math -

    not an answer, but steve, how did you get sqrt of 182.88? just wondering.

  • Math -

    square 10.42 and 8.62 and add to get 182.88

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