How to find the surface area of a spherical triangle?

[prinsinn]

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.

 

[Gib Z]

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).

 

[FleetFoot]

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.

 

[tiny-tim]

hello prinsinn!

(have a pi: π )

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

 

[HallsofIvy]

Did you remember to convert the angles to radians?