  Let alpha be an arbitrary angle in a random spherical triangle Delta and a be
the side opposite alpha. (The sphere has radius 1; vertices of Delta are
independent and uniform.) If some other side is constrained to be pi/2, then
E(alpha*a)=3.05.... If instead some other angle is fixed at pi/2, then
E(alpha*a)=2.87.... In our study of the latter scenario, both Apery's constant
and Catalan's constant emerge. We also review Miles' 1971 proof that
E(alpha*a)=pi^2/2-2 when no constraints are in place.
