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Trigonometry question

  1. May 21, 2013 #1
    1. The problem statement, all variables and given/known data

    As per the attachment


    3. The attempt at a solution

    for
    a) sin58° = 32/hyp
    hyp*sin58°=32
    hyp=32/sin58°
    hyp=32/0848
    hyp=37.73
    so to the nearest km between towns W & Y = 38km

    b)cosθ=adj/hyp
    cosθ=27/38
    cosθ=0.710
    θ=cos^-1(0.710)
    θ=44.76

    so to the nearest degree the angle = 45°

    c)?^2=38^2-27^2
    =√715
    =26.73

    so to the nearest km = 27km

    do these look correct? I'm not sure with the last answer as if it is 27km its the same size as the other side and that does not look correct.
     

    Attached Files:

  2. jcsd
  3. May 21, 2013 #2
    Your answers look correct to me.
     
  4. May 21, 2013 #3
    that last one just doesn't feel right, it look noticeably shorter than the known 27 km side
     
  5. May 21, 2013 #4
    It looks a little shorter, but how accurate is the diagram?
     
  6. May 21, 2013 #5
    true, it does not show any scale so it probably is correct maybe me overthinking it.
     
  7. May 21, 2013 #6
    I think it's just the diagram - e.g. the right angle at the bottom is not accurate.
     
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