A vessel at LAT 18° 54' N, LONG 73° 00' E,...

Question 1 of 2707066636eea28f7522a1c51b7c0

A vessel at LAT 18° 54' N, LONG 73° 00' E, heads for a destination at LAT 13° 12' N, LONG 54° 00' E. Determine the true course and distance by Mercator sailing.

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Question 1 of 27070

A vessel at LAT 18° 54' N, LONG 73° 00' E, heads for a destination at LAT 13° 12' N, LONG 54° 00' E. Determine the true course and distance by Mercator sailing.

🔍 Key Concepts

• Mercator sailing relationships between difference of longitude, meridional parts, and course • Using meridional parts (M) for each latitude and finding difference of meridional parts (ΔMP) • Relationship in Mercator sailing: $\tan(C) = \frac{\Delta \text{Long}}{\Delta \text{MP}}$ and distance from $D = \frac{\Delta \text{Lat}}{\cos C}$ (with proper units)

💭 Think About

• First, decide which point is the departure and which is the destination, then find the difference in latitude and difference in longitude with correct signs (N/S, E/W). How do these signs affect the quadrant of your course? • Look up or calculate the meridional parts for the starting and ending latitudes. What do you get for ΔMP, and does it make sense compared to your ΔLat? • After you compute the course from the tangent ratio, think: is your answer a NE, SE, SW, or NW course based on how latitude and longitude are changing? Which of the options fits that quadrant and distance range?

✅ Before You Answer

• Be sure the difference of longitude (ΔLong) is converted to minutes (or degrees consistently) before using it in the tangent ratio. • Confirm you are using the difference of meridional parts (ΔMP), not just the simple difference in latitude, in the Mercator sailing formula. • After finding the course angle from the arctangent, check that you place it in the correct true bearing (0°–360°) according to the direction of travel (increasing/decreasing latitude and longitude).