Spherical Triangle: Sum of Two Sides is Always Bigger than Third Side

[prinsinn]

Do you know any good example (or proof) that shows that the sum of two sides is alwasys bigger than the third side in a spherical triangle.

 

[robphy]

spherical "law of cosines"

 

[HallsofIvy]

How about simply "a straight line is the shortest distance between two points"?

 

[GleefulNihilism]

Think about the converse. What is a triangle like when the third side is equal to or less then the 2 other sides put together?