The great circle distance from LAT 25°50'N,...

Question 1 of 2921866636eea28f7522a1c51b2e4

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. Determine the longitude of the vertex, given the latitude of the vertex as 37°34.9'N.

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Question 1 of 29218

🔍 Key Concepts

• Great circle vertex: highest latitude point on a great circle between two positions • Relationship between initial course, vertex latitude, and difference of longitude on a great circle • Using meridional parts / spherical trig to relate course, latitude, and longitude on a great circle leg

💭 Think About

• How can you use the known initial course at departure and the latitude of the vertex to find the change in longitude from the departure point to the vertex? • What trigonometric relationship connects course, latitude of departure, and latitude of vertex on a great circle (think of Napier’s rules or standard great-circle vertex formula)? • Once you find the difference of longitude from the starting point to the vertex, how do you apply the correct east/west sign to get the vertex longitude?

✅ Before You Answer

• Be sure you are using departure latitude and vertex latitude in the correct positions of the formula (don’t mix them up). • Check that your computed difference of longitude is reasonable for a route from the Bahamas toward the Strait of Gibraltar (should still be in the western hemisphere at the vertex). • Confirm that you correctly convert between degrees and minutes and handle rounding so your final longitude matches one of the options.