Departure along a parallel — distance between widely separated longitudes at high latitude Two places at latitude 60° N have longitudes 93° E and 97° W. What is their departure (distance along that parallel) expressed in nautical miles?

Introduction / Context:
In navigation and geodesy, the east–west separation of two points at the same latitude is called the departure along the parallel. It depends on the longitude difference scaled by the cosine of latitude because parallels shrink toward the poles.

Given Data / Assumptions:

• Latitude φ = 60° N.
• Longitudes λ1 = 93° E, λ2 = 97° W → longitude difference Δλ = 190°.
• 1° of arc on a great circle equals 60 nautical miles (NM).

Concept / Approach:

Distance along a parallel = (Δλ in degrees) * 60 NM/degree * cos φ. The cosine factor reduces the length compared to the equator because the circumference of a latitude circle is smaller than Earth’s equator by cos φ.

Step-by-Step Solution:

Verification / Alternative check:

The equatorial distance for 190° would be 11,400 NM; halving at 60° latitude gives 5,700 NM, consistent with the computation.

Why Other Options Are Wrong:

• 5,100 NM underestimates because it uses an incorrect cosine or angle.
• 120 NM and 500 NM are off by an order of magnitude.
• “None of these” is incorrect because a correct numeric choice exists.

Common Pitfalls:

• Forgetting to use the smaller of Δλ and 360° − Δλ; here Δλ = 190° is correctly used because it is the smaller angular separation across the globe along the chosen direction.

Final Answer:

5,700 nautical miles.