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Homework Help: Vector Addition problem?

  1. Sep 7, 2011 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://img6.imageshack.us/img6/4057/pictureforforums.png [Broken]
    A hiker walks 8.33 km 30 degrees N of E then 4.97 km 45 degrees N of W and finally 7.32 km 60 degrees S of E. How far and in what direction is the hiker from the original position (A) to (B)

    2. Relevant equations

    Not sure if any, I used Law of Sines and Cosines

    3. The attempt at a solution

    As you can see in the picture, I subtracted 4.97 km from 7.32 km to get 2.35 km, I did this because N of W and S of E are opposites, not sure of right on that part though. So then I get a triangle with lenghts 8.33, and 2.35, and an angle of 30, Using Law of Sines

    [itex]\stackrel{8.33}{sin(30)}[/itex] = [itex]\stackrel{2.35}{sin(b)}[/itex]

    which gives B = 8.10898 degrees,

    angles A B and C have to add up to 180 so C is 141.891

    Law of Cosines is

    c = [itex]\sqrt{8.33^2 + 2.35^2 - 2(8.33*2.35)cos141.891}[/itex] = 10.2819 km
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 7, 2011 #2
    Solve by breaking up into components - law of cosines is not needed.
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