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How To Find Sides Of Right Triangle With Known Angles And Area?

  1. Jul 23, 2009 #1
    I'm comparing TV and monitor sizes, and I'm trying to figure out the formula that will let me find what size screen will have the same area as another screen (with different aspect ratios). This boils down to a right triangle with all the angles and the area known. Normally I'd find this on Google, but there are a large number of pages describing how to find the area with known sides or areas that are getting in the way.

    So can someone post the formula for this?
     
  2. jcsd
  3. Jul 23, 2009 #2
    Let a be the adjacent, let b be the opposite, and let c be the hypotenuse and A the area. Then

    [tex]
    \[
    c = \sqrt{\frac{2A}{\cos \theta \sin \theta}}
    \]
    \[
    a= \sqrt{2A \cot \theta}
    \]
    \[
    b = \sqrt{2A \tan \theta}
    \]
    [/tex]
     
    Last edited: Jul 23, 2009
  4. Jul 24, 2009 #3
    Perfect, thanks.
     
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