Calcs

 

There we have it: the formula for the aea of the triangle: the three triangle angles

minus pi, then multiply by R^2.

Finding those surface angles requires some work with trigonometric identities,

We keep in mind that - working with radians - the length of the sides are also

the angle measure of the sphere center angles.

                                                           *     *     *

Found a calculator for those surface angles. It is in German, but Google will

trnaslate to English.

Entered angle sides of 30, 30, 20 and a radius of 50. 

                                                                 

 

http://www.in-dubio-pro-geo.de/?file=plasph/stri0