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Calcular la distancia ortodrómica que separa los puntos de coordenadas 33° 41′ S, 132° 27′ E y 16° 19′ N, 081° 52′ W.Calculate the great-circle distance separating the points 33° 41′ S, 132° 27′ E and 16° 19′ N, 081° 52′ W.
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Correct answer: c) 8678′
Why it is correct
The shortest difference of longitude is ΔL = 360º − (132º 27′ + 81º 52′) = 145º 41′. With opposite-name latitudes, cos D = −sin(33º 41′) sin(16º 19′) + cos(33º 41′) cos(16º 19′) cos(145º 41′) = −0.81541, giving D = 144.627º = 8678′.
Why the others are not
- a) Takes the supplement of the arc (180º − D) instead of D.
- b) Adds the sine product as if the latitudes had the same name.
- d) Does not match the spherical law of cosines.
How to work it out in the exam
- When cos D is negative, D is obtuse (> 90º, over 5400 miles).
Where this question comes from
- Junta de Andalucía · 2022 · 3ª convocatoria · CY Módulo de navegación · question 18 Official paper · Official answer key
Pending instructor review. Machine translation, not reviewed.