The great circle distance from LAT 25°50'N, LONG 77°00'W to LAT 35°56'N, LONG 06°15'W is 3616 miles, and the initial course is 061.7°T. The position of the vertex is LAT 37°34.9'N, LONG 25°59.0'W. The difference of longitude from the vertex to a point (X) on the great circle track is 10°W. Determine the latitude which intersects the great circle at point (X).

Question

The great circle distance from LAT 25&deg;50'N, LONG 77&deg;00'W to LAT 35&deg;56'N, LONG 06&deg;15'W is 3616 miles, and the initial course is 061.7&deg;T. The position of the vertex is LAT 37&deg;34.9'N, LONG 25&deg;59.0'W. The difference of longitude from the vertex to a point (X) on the great circle track is 10&deg;W. Determine the latitude which intersects the great circle at point (X).

Accepted Answer

Option A: 37&deg;09.5'N. The latitude of a point on a great circle track is found using the formula tan(Lat) = cos(DLo) * tan(Lat_vertex). Given the vertex latitude of 37°34.9'N and a difference of longitude of 10°, the calculation yields a latitude of 37°09.5'N for point X.