The great circle distance from LAT 38°17'N,...

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Question 1 of 2066636eea28f7522a1c51b2ec

The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°T. Determine the latitude of the vertex.

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Question 1 of 20

66636eea28f7522a1c51b2ec

The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°T. Determine the latitude of the vertex.

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🔍 Key Concepts

• Great-circle vertex occurs where the track is due east or west (course 090°T or 270°T), and this is the maximum latitude reached on the great circle. • For great-circle sailing, there is a standard relationship between departure latitude, initial great-circle course, and the vertex latitude (see the great-circle/vertex formulas in Bowditch). • The vertex latitude must be poleward of both the departure and arrival latitudes for this North Pacific route.

💭 Think About

• Think about how the ship’s track behaves leaving 38°17'N on an initial course of 300.9°T: does it first go more northward or more westward, and what does that suggest about how far north the vertex can be? • Use the standard great-circle formula that ties together departure latitude and initial course to solve for the vertex latitude, then compare your computed value to the options. • After you estimate the vertex latitude, ask yourself: is it reasonably higher than both 38°17'N and 35°01'N, but still realistic for a trans-Pacific great-circle between these longitudes?

✅ Before You Answer

• Be sure you are using the initial great-circle course at departure, not the course at arrival, in your vertex calculation. • Confirm that your trigonometric functions (sine/cosine) are using degrees and that you enter the latitude as north-positive. • When you obtain a numerical latitude, check that it is greater than both endpoint latitudes but still a plausible maximum latitude for this route before matching it to the nearest choice.

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Question 1 of 2066636eea28f7522a1c51b2ec

The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°T. Determine the latitude of the vertex.

Back

Question 1 of 20

66636eea28f7522a1c51b2ec

The great circle distance from LAT 38°17'N, LONG 123°16'W to LAT 35°01'N, LONG 142°21'E is 4330 miles, and the initial course is 300.9°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

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