Distancia ortodrómica entre los puntos de coordenadas 47º 39′ S, 91º 52′ E, y 18º 21′ N, 103º 46′ W.Great-circle distance between the points 47º 39′ S, 91º 52′ E and 18º 21′ N, 103º 46′ W:

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Distancia ortodrómica entre los puntos de coordenadas 47º 39′ S, 91º 52′ E, y 18º 21′ N, 103º 46′ W.Great-circle distance between the points 47º 39′ S, 91º 52′ E and 18º 21′ N, 103º 46′ W:

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Correct answer: d) 8882'

Why it is correct

Crossing the antimeridian, ΔL = 360º − (91º 52′ + 103º 46′) = 164º 22′. With latitudes in opposite hemispheres, cos D = −sin(47º 39′) sin(18º 21′) + cos(47º 39′) cos(18º 21′) cos(164º 22′) = −0.84842, giving D = 148.040º = 8882′.

Why the others are not

a) Confuses the distance with the 1852 metres in one nautical mile.
b) Treats cos(164º 22′) as positive instead of negative.
c) Applies the wrong signs to the sine and cosine products.

How to work it out in the exam

Here both terms of cos D are negative (opposite hemispheres and ΔL > 90º).

Where this question comes from

Junta de Andalucía · 2023 · 2ª convocatoria · CY Módulo de navegación · question 12 Official paper · Official answer key

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Pending instructor review. Machine translation, not reviewed.