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Math Help - The Bearing of a Line

  1. #1
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    The Bearing of a Line

    Ypsilanti, Michigan, is 60 mi due north of Bowling Green, Ohio. A helicopter leaves Bowling Green at 3 PM and travels 40 mi/h in the direction 338. When will it be closest to Ypsilanti?
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  2. #2
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    Re: The Bearing of a Line

    BG,Y and point of landing helcopter makes rectangular triangle. Use trigonometry
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  3. #3
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    Re: The Bearing of a Line

    A more common phrase would be "right triangle". But, yes, knowing the angle, the length of the hypotenuse is 60 and the near leg is 40t where t is the number of hours the helicopter is flying, you can find the length of the "opposite leg" using trigonometry.
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  4. #4
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    Re: The Bearing of a Line

    If I draw a right triangle, I can find that the hypotenuse through

    h = 60 / (cos 22) = 65 mi (rounded)

    speed = distance / time

    time = 65 mi / (40 mi/h) = 1.625 hour = 98 minutes (rounded)

    Due to my calculations, the helicopter will be closest to Ypsilanti at 4:38 P.M.

    But the book says 4:23 P.M.

    What am I missing?
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  5. #5
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    Re: The Bearing of a Line

    Round closer
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  6. #6
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    Re: The Bearing of a Line

    Sorry guys, I made the hypotenuse the wrong Leg. If the hypotenuse is the 60 miles distance between the two cities then the answer will be 4:23 P.M.

    My Question now is

    How did we manage to make the 60 miles distance between them, is the hypotenuse?
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  7. #7
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    Re: The Bearing of a Line

    By a
    Picture
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  8. #8
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    Re: The Bearing of a Line

    The plane flies 22 deg east of north.It will be closest to Ypsilanti when that city is due west of planes position after it travels 64.7 miles in 1 hour 37 minutes ( 4:37 PM.) At that time Ypsilanti is 24.2 miles away
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  9. #9
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    Re: The Bearing of a Line

    bjhopper,

    You made the same mistake that I made.

    The plane will not be the closest when it is west of Ypsilanti (horizontally left of it), but it will be closest Before that (approximately 55 miles plane travels).
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