229. The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 22° 36.0' N, LONG 128° 16.0' E is 7801 miles and the initial course is 318° 45' T. The latitude of the vertex is 49° 20.6' N. What is the longitude of the vertex?

The vertex longitude is calculated using the formula cos (Δλ) = tan φ1 / tan φv, where φ1 is the departure latitude and φv is the vertex latitude. Applying this formula with the given latitudes yields a longitude difference of 82 20', which, when added to the departure longitude of 80 21' W, results in a vertex longitude of 162 41' W.