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Math Help - Find the distance

  1. #1
    Junior Member
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    Find the distance

    A ship travels 55 km on a bearing of 27 degree, then travels on a bearing of 117 degree for 140 km. Find the distance traveled from the starting point to the ending point.
    ******************************************
    What I did is following:
    sin27=55/hypotenuse
    cos63=55/hypoenuse
    *****>>>>these two give me 121 km
    cos27=140/hypotenuse
    Sin63=140/hypotenuse
    *****>>>>>these two give me 157 km
    But if I used the pythagorean thm, it gives me 150 km

    I have seen similar problems they used sometimes, cos or sin or solve by pythagoran thm........It's confusing when to use what?
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  2. #2
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    from your explanation I found you could just use the pythagoras theorem with 55 and 140 as the shorter sides as the turn of the ship was exactly 90 degrees, therefore

    distance travelled = \sqrt{55^2+140^2} = 150.42

    The 157 could've resulted in rounding error introduced from using the trig functions.
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by Judi View Post
    A ship travels 55 km on a bearing of 27 degree, then travels on a bearing of 117 degree for 140 km. Find the distance traveled from the starting point to the ending point.
    ******************************************
    What I did is following:
    sin27=55/hypotenuse
    cos63=55/hypoenuse
    *****>>>>these two give me 121 km
    cos27=140/hypotenuse
    Sin63=140/hypotenuse
    *****>>>>>these two give me 157 km
    ...
    Have you made a sketch?

    The bearings are outside of the triangle in question. Therefore your method will not provide you with a valid result.
    Attached Thumbnails Attached Thumbnails Find the distance-entfernung.png  
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