The great circle distance from LAT 24°25.3'N, LONG 83°02.6'W to LAT 35°57.2'N, LONG 5°45.7'W is 3966.5 miles. Determine the latitude of the vertex.

Correct Answer: Option C — 38°09.4'N

Great circle sailing vertex latitude is derived using spherical trigonometry formulas from Bowditch. The relationship involving initial course angle and departure latitude, $\cos(Lat_{vertex}) = \sin(Course) \times \cos(Lat_{start})$, determines the maximum latitude reached along the great circle arc as 38°09.4'N.