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I need someone to explain this vector question's answer

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Vectors A and B have equal magnitudes of 57. If the sum of A and B is the vector 16.3j , determine the angle?



    3. The attempt at a solution
    I have already gotten the answer
    2•57cosθ = 16.3
    cosθ = 0.143
    θ = 81.8º
    twice that is the angle between them, or 163.6º
    but at first i did 2*57sinθ=16.3 since we have the y component and as far as I know y=rsinθ
    why is the right answer cos?
     
  2. jcsd
  3. Feb 25, 2012 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    So draw the diagram, in 2 dimensions. Since the vectors are of equal length, and their x components cancel, the second vector must be a reflection of the first in the y axis.

    Working without a sketch of what you are dealing with is a dangerous thing! If you refer to your diagram, you will see that y=rsinθ only if θ is the other acute angle in the triangle. So rsinθ will find you the complementary angle of what you are needing here.

    It all becomes clear when you draw a diagram.
     
  4. Feb 26, 2012 #3
    Thank you! you were right! I got it now
     
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