You are on a great circle track departing from position LAT 25°50'N, LONG 77°00'W. The position of the vertex is LAT 37°35.6'N, LONG 25°57.8'W. The distance along the great circle track from the vertex to a point (X) is 600 miles westward. Determine the position of point (X) on the great circle track.

Question

You are on a great circle track departing from position LAT 25&deg;50'N, LONG 77&deg;00'W. The position of the vertex is LAT 37&deg;35.6'N, LONG 25&deg;57.8'W. The distance along the great circle track from the vertex to a point (X) is 600 miles westward. Determine the position of point (X) on the great circle track.

Accepted Answer

Option A: LAT 36&deg;55.6'N, LONG 38&deg;30.0'W. Using the formulas for great circle sailing from a vertex, the latitude and longitude of a point at a specific distance from the vertex are found using spherical trigonometry. Applying the 600-mile distance along the track from the vertex at 37°35.6'N, 25°57.8'W yields the position 36°55.6'N, 38°30.0'W.