The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°T. Determine the latitude of the vertex.

Question

The great circle distance from LAT 38&deg;17'N, LONG 123&deg;16'W to LAT 35&deg;01'N, LONG 142&deg;21'E is 4330 miles, and the initial course is 300.9&deg;T. Determine the latitude of the vertex.

Accepted Answer

Option C: 47&deg;40.5'N. The vertex of a great circle is the point of highest latitude. Using the spherical trigonometry formula sin(Lat_v) = cos(Lat_1) * sin(Initial_Course), where the initial course is 300.9°T, the latitude of the vertex is calculated to be 47°40.5'N, representing the apex of the shortest distance arc.

The great circle distance from LAT 38&deg;17'N, LONG 123&deg;16'W to LAT 35&deg;01'N, LONG 142&deg;21'E is 4330 miles, and the initial course is 300.9&deg;T. Determine the latitude of the vertex.

The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°T. Determine the latitude of the vertex.