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Sine rule using cross product

  1. Oct 20, 2009 #1
    Could any one tell me how to use the cross product to prove the sine rule
     
  2. jcsd
  3. Oct 20, 2009 #2

    rl.bhat

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    Area of a triangle of side a.b and c is
    A = 1/2*axb = 1/2absinC
    Similarly 1/2*bxc = 1/2 bcsinA and so on
    So
    absinC = bcsinA = casinB. Dividing abc to all we get
    sinA/a = sinB/b = sinC/c
     
  4. Oct 20, 2009 #3
    Here AB,BC,CA ,a,b,c are vectors and AB=a BC=b CA=c
    in a triangle ABC,
    AB + BC + CA = 0
    a + b + c= 0
    a x b =b x c = c x a(proved using above statement just take b and c to other side and take crossproduct with b on both sides first and then with c)
    la x bl= |b x c|= |c x a |
    |a||b| SinC= |b||c|SinA=|a||c| SinB
    dividing by |a||b||c|
    we get Sine formula
     
    Last edited: Oct 20, 2009
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