The great circle distance from LAT 35°08.0'S, LONG 19°26.0'E to LAT 33°16.0'S, LONG 115°36.0'E is 4559 miles and the initial course is 121°T. Determine the longitude of the vertex.

Correct Answer: Option A — 65°45.9'E

Using Napier's Rules for spherical triangles, the vertex longitude is found by solving the right spherical triangle formed by the initial position, the vertex, and the pole. The calculation for the vertex longitude, given the initial course and coordinates, results in 65°45.9'E.