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A ship travels due north for 25 miles then changes course to a bearing of 300°. It travels on this path for 29 miles. How far is the ship from where it started?

  • Math -

    Sum the east (x-) and north (y-) components.

    x=∑D cos(θ)
    =25*cos(90°)+29 cos(90-300°)
    =0+29cos(-210)
    =-(29/2)√3

    y=∑D sin(θ)
    =25*sin(90°)+29sin(90-300°)
    =25+29sin(-210°)
    =25+29sin(30°)
    =25+14.5
    =39.5

    Distance
    =sqrt(x^2+y^2)
    =...

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