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AAA Triangle

  1. Jan 12, 2009 #1
    1. The problem statement, all variables and given/known data
    All three sides of an isoceles triangle are given along with its perimeter. Find the length of each side.
    A=97.433 B=41.283 C=41.283

    2. Relevant equations
    p = a+b+c
    a2=b2+c2 - 2*b*c*cos(A)

    3. The attempt at a solution
    Would you somehow find the ratios of the side lengths? And then use the ratios and the perimeter to find the sides? I don't even know if this is possible. We definitly never did these kinds of triangles in geometry class. Thanks for any help :)
  2. jcsd
  3. Jan 12, 2009 #2


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    I see you listed the law of cosines in the equations... but forgot the law of sines....
  4. Jan 12, 2009 #3
    Law of sines: c/sin(A) = c/sin(B) = c/sin(C)

    Do I have to solve this as a system of equations to solve for the sides? But where does the given perimeter come into play?
  5. Jan 12, 2009 #4


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    You have many equations:
    a+ b+ c= 24.78
    b= c
    [tex]c^2= a^2+ b^2- 2abcos(41.283)[/tex]
    [tex]b^2= a^2+ c^2- 2accos(41.283)[/tex]
    [tex]a^2= b^2+ c^2- 2bccos(97.433)[/tex]
    [tex]\frac{a}{sin(97.433)}= \frac{b}{sin(41.283)}[/tex]
    [tex]\frac{a}{sin(97.433)}= \frac{c}{sin(41.283)}[/tex]
    [tex]\frac{b}{sin(41.283)}= \frac{c}{sin(41.283)}[/tex]
    Of course, these are not all independent.
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