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Prove Heron's Formula (Trigonometry)

  1. Aug 26, 2007 #1
    1. The problem statement, all variables and given/known data

    If a, b, c are the lengths of the sides of a triangle, then the area K of the triangle is given by [tex]K=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{1}{2}(a+b+c)[/tex]. The number s is called the semiperimeter. Prove Heron's Formula. Hint: Use the area formula [tex]K=\frac{1}{2}bc\sin\phi[/tex].

    sinphi should be sinA. it wouldn't let me use sinA.

    3. The attempt at a solution

    Absolute torture if you ask me!!! I need help getting on the right track, any help is appreciated.

    Ignore everything from the triangle and down, that's a different problem.

    [​IMG]
     
    Last edited: Aug 26, 2007
  2. jcsd
  3. Aug 26, 2007 #2
    my way:
    K=whatever
    K^2=whatever without sqrt

    K^2 = that sin theta area^2

    and using identidy sin^2 = 1-cos^2 in above

    and cosine law, and some simplication, you would eventually reach somewhere like
    -a^4+6a^3+3a^2......

    and now just expand that herione thing

    lol >(evil smile)<
     
  4. Aug 26, 2007 #3
    lol ... i don't follow!!! :surprised
     
  5. Aug 26, 2007 #4
    you didn't square the equation in the starting, but I did..
     
  6. Aug 26, 2007 #5
    ok let me try it that way.
     
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