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How to find the surface area of a spherical triangle?

  1. Nov 6, 2007 #1
    Hello

    I have a spherical triangle with the radius 1, and I have tried so hard to find the surface area. I know that A=120°, b=90° and c=60°.

    I could calculate that B=73.89° and C=56.31° and a=115.66°.

    I think I should use the formula
    (ABC) = (A + B + C - pi) r2

    I always get the wrong answer but the correct one is 1.2254.

    Can someone please tell me what to do, thanks.
     
  2. jcsd
  3. Nov 7, 2007 #2

    Gib Z

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    Go on Wikipedia and Look up some of Gausses work on Spherical Trig, it should have an analogous result to Euclidean Planes area of a triangle (half a b sine c).
     
  4. Nov 29, 2010 #3
    Girard's Theorem states that the sum of the angles of a triangle drawn on a sphere is not 180 degrees but the sum differs from 180 degrees by the area of the triangle divided by the radius squared.
     
  5. Nov 29, 2010 #4

    tiny-tim

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    hello prinsinn! :smile:

    (have a pi: π :wink:)
    well, your formula is correct, and using your A B and C i do get 1.2254 :confused:
     
  6. Nov 29, 2010 #5

    HallsofIvy

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    Did you remember to convert the angles to radians?
     
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