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

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Question 1 of 2066636eea28f7522a1c51b2df

The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 12° 36.0' N, LONG 128° 16.0' E is 8664 miles, and the initial course is 306.6° T. Determine the latitude of the vertex.

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Question 1 of 20

66636eea28f7522a1c51b2df

The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 12° 36.0' N, LONG 128° 16.0' E is 8664 miles, and the initial course is 306.6° T. Determine the latitude of the vertex.

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🔍 Key Concepts

• Great circle and vertex: the vertex is the point of highest latitude along a great circle track • Relationship between initial course at the departure point and the maximum latitude reached on the great circle • Use of meridional parts / spherical trigonometry: ( \sin(\text{Lat}_\text{vertex}) = \sin(\text{Lat}1) / \cos(C\text{initial}) ) for a great circle

💭 Think About

• How does the initial course being significantly different from due east or west affect how far north the great circle will bend? • Given the departure latitude and the initial course, what trigonometric relationship links them to the latitude of the vertex? • Once you compute a value for the latitude of the vertex in degrees and minutes, which option is closest while still being consistent with your calculator work?

✅ Before You Answer

• Be sure you convert the initial course to the proper angle for use in cosine (check whether you need (C), (90^\circ - C), or (C - 90^\circ)) • Double-check that your sine value for the vertex latitude is between -1 and +1 before taking (\sin^{-1}) • Verify your final latitude is north of both departure and arrival latitudes, since the track bends toward higher latitude in this case

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Question 1 of 2066636eea28f7522a1c51b2df

The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 12° 36.0' N, LONG 128° 16.0' E is 8664 miles, and the initial course is 306.6° T. Determine the latitude of the vertex.

Back

Question 1 of 20

66636eea28f7522a1c51b2df

The great circle distance from LAT 08° 50.0' N, LONG 80° 21.0' W to LAT 12° 36.0' N, LONG 128° 16.0' E is 8664 miles, and the initial course is 306.6° T. Determine the latitude of the vertex.

No comments yet

Be the first to share your thoughts!

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?

Quick actions

— No credit card needed