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. Determine the latitude intersecting the great circle track 600 miles west of the vertex, along the great circle track.

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. Determine the latitude intersecting the great circle track 600 miles west of the vertex, along the great circle track.

Accepted Answer

Option D: 36&deg;54.9'N. Using the haversine or cosine formula for great circle navigation, the latitude of a point on the track is determined by the vertex latitude and the difference in longitude from the vertex. Applying the spherical trigonometry formula cos(Lat) = cos(Vertex Lat) * cos(Diff Long) yields the latitude 36°54.9'N.