436. The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 12° 36.0' N, LONG 128° 16.0' E is 8664 miles, and the initial course is 306.6° T. Determine the latitude of the vertex.

The vertex latitude is determined using the great circle invariant, which states that the product of the cosine of the latitude and the sine of the course is constant. Setting the course to 90 degrees at the vertex allows calculation of the latitude as 37 30.2' N.