Find the distance between this pair of points o... - SS3 Mathematics Longitude and Latitude Question
Find the distance between this pair of points on the earth surface: \(P(56{^\circ}N,\ \ 43{^\circ}W)\) and \(Q(56{^\circ}N,\ \ 17{^\circ}E)\). Take \(R = 6,400km\) and \(\pi = 3.142\)
A
6,550km
B
3,748km
C
3,412.90km
D
6,704.76km
correct option: b
Given \(P(56{^\circ}N,\ \ 43{^\circ}W)\) and \(Q(56{^\circ}N,\ \ 17{^\circ}E)\):
\[d = \frac{\alpha}{360} \times 2\pi R\cos\theta\]
\[\alpha = 43{^\circ} + 17{^\circ} = 60{^\circ}\]
\[R = 6,400km\]
\[\pi = 3.142\]
\[\theta = 56{^\circ}\]
\(d = \frac{60}{360} \times 2 \times 3.142 \times 6400{\times cos}{56{^\circ}} = 3,748\ km\)
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