Trigonometry

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If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?
A. 14 nm
B. 17.75 nm
C. 21.5 nm
D. 22.6 nm
PLEASE HELP!

  • Trigonometry -

    looks like a rather straight-forward case of the cosine law.
    distance^2 = 42^2 + 28^2 - 2(42)(28)cos60
    = 1372
    distance = 37.04 nm

    or

    vector of first leg = (42cos270, 42sin270)=(0, -42)
    vector for 2nd leg = (28cos30,28sin30) = (24.249, 14)
    adding them to get (24.249 , -28)
    magnitude = √(24.249^2 + (-28)^2) = √1372 = 37.04 nm

    None of your answers match this.
    My answer was obtained in 2 totally different methods

  • Trigonometry -

    Wel, I'm not sure, I have two other questions with practically the same things, please take a look!
    If a ship leaves port at 9:00 a.m. and sails due east for 3 hours at 10 knots, then turns N 60° E for another hour, how far from port is the ship?
    A. 35 nm
    B. 39 nm
    C. 43 nm
    D. 47 nm
    __________________________________
    If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?
    A. 14 nm
    B. 17.75 nm
    C. 21.5 nm
    D. 22.6 nm
    _____________________________
    Thank you; you'tr a life saver!

  • Trigonometry -

    If a ship leaves port at 9:00 a.m. and sails due north for 3 hours at 12 knots, then turns N 30° E for another hour, how far from port is the ship?
    A. 45 nm
    B. 47 nm
    C. 51 nm
    D. 53 nm

  • Trigonometry -

    This time I get a triangle with sides 30 and 10 and the contained angle between them is 150° , (90+60)

    again by the cosine law,
    dist^2 = 30^2 + 10^2 - 2(30)(10)cos150
    = 1519.62
    distance = √1519.62 = appr 38.98 nm
    which is choice B

    The next question you posted is a repeat of your first

    The third:
    same setup;
    dist^2 = 36^2+ 12^2 - 2(36)(12)cos150
    = 2188.25
    dist = 46.78 which looks like it is B.

    Something fishy about your first one, since I followed exactly the same steps
    check for data or answers.

  • Trigonometry -

    Thank you very much; but these are the only answers! I don't know why, but I'll try to check with my teacher. Again, thanks for the help and showing your work, you're awesome!

  • Trigonometry -

    Just tried you first question again, using cos30° in my cosine law
    and got 22.6 which is D

    BUT, according to your wording of N 60° E, the angle between the two paths would be 60, and not 30

    So to get your answer it should have been N 30° E

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