🔍 Key Concepts

• Great-circle vertex: point of highest latitude on the great-circle track where the course is due east or west (090°/270°). • On a great circle, the quantity cos(latitude) × sin(course) is constant along the track, and the vertex is where sin(course) = 1. • To get the vertex longitude, you need the difference of longitude from the departure to the vertex, then apply the correct E/W sense from the initial course and starting longitude.

💭 Think About

• Draw a rough sketch of the North Pacific, marking the departure, destination, and the vertex latitude. In which general quadrant (NE, NW, SE, SW) does the vertex lie? • From the given initial course of 300.9°T (NW’ly), think about whether the longitude of the vertex must be farther east or farther west than the departure longitude of 123°16.0'W. • Once you determine the difference of longitude from the departure to the vertex, how do you decide whether to add or subtract it from 123°16.0'W, and how does that affect whether the result should be labeled E or W?

✅ Before You Answer

• Confirm you are using the vertex latitude (47°40.5'N) together with the departure latitude (38°17.0'N) and the initial course (300.9°T), not the arrival latitude, in your great-circle relationships. • Be sure your final longitude is consistent with your sketch of the track (you should be able to see whether the vertex should be east or west of the 180° meridian). • Check that the numerical longitude you obtain exactly matches one of the choices, including the correct hemisphere (E or W) and minutes.