The great circle distance from LAT 38°17.0'N, LONG 123°16.0'W to LAT 35°01.0'N, LONG 142°21.0'E is 4330 miles and the initial course is 300.9°T. The latitude of the vertex is 47°40.5'N. What is the longitude of the vertex?

Correct Answer: Option C — 167°18.5'W

Applying the spherical trigonometry formula for the vertex of a great circle, cos(Δλ) = tan(Lat_1) / tan(Lat_v), with Lat_1 = 38°17.0'N and Lat_v = 47°40.5'N, the difference in longitude is 44°02.5'. Adding this to the departure longitude of 123°16.0'W results in 167°18.5'W.