Ajay is standing at point $A$, $60^\circ$ N latitude and $0^\circ$ longitude. Billy is standing at point $B$, $60^\circ$ N latitude and $180^\circ$ longitude. Assume Earth is a perfect sphere with center $C$. What is the degree measure of $\angle ACB$?

1. With both latitudes $60^\circ$N and longitudes exactly $180^\circ$ apart: $\cos\angle ACB=\sin60^\circ\sin60^\circ+\cos60^\circ\cos60^\circ\cos180^\circ=\frac34-\frac14=\frac12$.
2. So $\angle ACB=60^\circ$.