Check this Geogebratube offering: a right triangle on a sphere has a Pythagorean Theorem which, instead of a^2 + b^2 = c^2 is (cos a)(cos b)=(cos c).

For small right triangles, the spherical version gives the familiar plane geometry formula–just use the power series for cosine, and ignore high-powered terms… and don’t forget to change the degrees to radians.

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