How to find the surface area of a spherical triangle?

  • Thread starter prinsinn
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  • #1
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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.
 

Answers and Replies

  • #2
Gib Z
Homework Helper
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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).
 
  • #3
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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.
 
  • #4
tiny-tim
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hello prinsinn! :smile:

(have a pi: π :wink:)
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.
well, your formula is correct, and using your A B and C i do get 1.2254 :confused:
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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Did you remember to convert the angles to radians?
 

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