The great circle distance from LAT 08° 50.0'...

Question 1 / 2066636eea28f7522a1c51b2e0

Question 1 of 2066636eea28f7522a1c51b2e0

The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 22° 36.0' N, LONG 128° 16.0' E is 7801 miles and the initial course is 318° 45' T. The latitude of the vertex is 49° 20.6' N. What is the longitude of the vertex?

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🔍 Key Concepts

• Great circle and vertex: Understand what the vertex of a great circle is (the point of maximum latitude) and how it relates to the great circle track between two positions. • Relationship between course and meridians: At the vertex, the great circle track is at right angles to the meridian (course = 090°/270° relative to the local meridian). Use this with the given initial course and vertex latitude. • Spherical trigonometry on the meridian: Use the formula that relates the difference of longitude between the vertex and departure point to their latitudes and the initial course at departure.

💭 Think About

• How does the fact that the latitude of the vertex is given (49° 20.6' N) help you find how far in longitude it is from the starting point? Think about how latitude changes along a great circle. • What trigonometric relationship connects the initial course, the departure latitude, and the vertex latitude to the difference in longitude between departure and vertex? • Once you compute the difference in longitude from the starting longitude, in which direction (east or west) should you move to get the vertex longitude, given that the vertex must lie between the two endpoints of the great circle track?

✅ Before You Answer

• Write down and carefully use the relationship: sin(lat of vertex) = cos(initial course) × sec(departure latitude) or its equivalent form; confirm you’re applying it with the correct units (degrees vs radians). • After finding the difference in longitude from the departure point to the vertex, check the sign and sense: does your vertex longitude lie in the correct hemisphere and between the longitudes of the two endpoints when following the great circle? • Compare your computed longitude with all four options and confirm the one that best matches, paying attention to minutes and rounding of your intermediate trigonometric values.

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Question 1 of 20

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Question 1 / 2066636eea28f7522a1c51b2e0

Question 1 of 2066636eea28f7522a1c51b2e0

Back

Question 1 of 20

66636eea28f7522a1c51b2e0

No comments yet

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If the question has a related picture, it will appear here.

🔍 Key Concepts

💭 Think About

✅ Before You Answer

👋 Hi! I'm Genie, your AI study assistant. How can I help you with this question?

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