The great circle distance from LAT 35° 57.2'...

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Question 1 of 2066636eea28f7522a1c51b2eb

The great circle distance from LAT 35° 57.2' N, LONG 05° 45.7' W to LAT 24° 25.3' N, LONG 83° 02.6' W is 3966.5 miles and the initial course is 283.7° T. The latitude of the vertex is 38° 09.4' N. What is the longitude of the vertex?

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Question 1 of 20

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🔍 Key Concepts

• Great-circle vertex definition: point of highest latitude on a great-circle track between two points • Relationship between vertex latitude, initial course, and difference of longitude (DLo) along a great circle • Using the meridian of the vertex and how its longitude relates to the departure point's longitude

💭 Think About

• How can you use the given initial course at the departure point and the known latitude of the vertex to find the change in longitude from the departure point to the vertex? • What great-circle triangle (with which vertices) can you form that includes the vertex, and which navigational formulas relate the sides (latitudes) and angles (courses/longitudes)? • Once you find the difference of longitude between the departure point and the vertex, how do you determine whether to add or subtract it from the departure longitude to get the vertex longitude?

✅ Before You Answer

• Be sure you are using vertex latitude (38° 09.4' N), not the latitudes of departure or destination, in the key formula • Confirm the sign of DLo (east or west) based on the geometry of the track and the initial course (283.7° T) from 05° 45.7' W • After computing the vertex longitude, check that it lies between the longitudes of the two endpoints in a way that makes geographic sense for a North Atlantic great-circle route

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