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Unknown lengths of triangle, known area and internal angles

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data

    I know the area of a right angled triangle, I also know the ratio of the two non-hypotenuse sides.
    Is there anyway of finding the lengths?

    Thanks!

    2. Relevant equations

    I don't think there are any like Area = 1/2abSinC

    3. The attempt at a solution

    I obviously know that tan of the ratio will give one angle, so I know the internal angles.

    buggered if I know, it's 2:45am here.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 4, 2013 #2

    pasmith

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    Homework Helper

    If the sides are [itex]a[/itex] and [itex]b[/itex] then you know that the area of the triangle is [itex]\frac12 ab[/itex].
     
  4. Nov 4, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If you call the two legs a and b then the area is (1/2)ab= A so ab= 2A.
    The ratio of the two sides is a/b= r so that a= br. Replace a in the first equation by that: ab= (br)b= rb^2= A so b^2= A/r. Solve for b, then solve for a.
     
  5. Nov 4, 2013 #4
    I DON'T know the sides, just the ratio of the sides (the gradient of the hypotenuse)
     
  6. Nov 4, 2013 #5
    Wow, that's brilliant, thanks very much!
     
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