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Calculate the shortest distance between two points P and Q on the parallel of latitude 34^ N with longitudes 27^ E and 12^ E respectively. Express your answer in Nautical Miles.

Geography

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Answer

746.1 NM746.1 \text{ NM}

Step-by-step solution

4 steps

  1. Identify the given coordinates.

    Latitude (ϕ\phi) for both P and Q is 34∘N34^\circ N.
    Longitude of P (λP\lambda_P) is 27∘E27^\circ E.
    Longitude of Q (λQ\lambda_Q) is 12∘E12^\circ E.

  2. Calculate the difference in longitude (θ\theta).

    Since both longitudes are in the same hemisphere (East), we subtract them.

    θ=∣27∘E−12∘E∣=15∘\theta = |27^\circ E - 12^\circ E| = 15^\circ

  3. Calculate the distance along the parallel of latitude in Nautical Miles (NM).

    The formula for the distance along a parallel of latitude in nautical miles is given by:

    Distance=60×θ×cos⁡(ϕ)\text{Distance} = 60 \times \theta \times \cos(\phi)

    where θ\theta is the difference in longitude in degrees, and ϕ\phi is the latitude.

    Substitute the values:

    Distance=60×15∘×cos⁡(34∘)\text{Distance} = 60 \times 15^\circ \times \cos(34^\circ) Distance=900×cos⁡(34∘)\text{Distance} = 900 \times \cos(34^\circ)

  4. Calculate the value.

    Using a calculator for cos⁡(34∘)\cos(34^\circ):

    cos⁡(34∘)≈0.8290\cos(34^\circ) \approx 0.8290 Distance=900×0.8290\text{Distance} = 900 \times 0.8290 Distance≈746.1 NM\text{Distance} \approx 746.1 \text{ NM}

    The shortest distance between P and Q along the parallel of latitude in Nautical Miles is:

    746.1 NM746.1 \text{ NM}
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