315. 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?

The vertex longitude is calculated using the formula cos (Δλ) = tan (φ) / tan (φv), resulting in a longitude approximately 44 west of the departure point. Adding this difference to the departure longitude of 12316.0'W yields the correct vertex longitude of 16718.5'W.