Kuulchat - Senior High School (S.H.S) Mathematics Latitude & Longitude Practice Test Questions

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LATITUDE & LONGITUDE

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1.

Two towns, U and V on the equator are on longitude 67°E and 124°E respectively.

(i)

Illustrate the information in a diagram.

(ii)

Find the distance between U and V along the equator.

(iii)

How far is U from the North pole?

[Take R = 6,400 and π = $\frac{22}{7}$ ]

Show Solution

(i)

(ii)

Distance between two points on earth

Distance = $\frac{Angular distance}{360}$ x 2 x π x R x cosθ

Where θ is the latitude, R is the radius of the earth and the angular distance is the angle between the two points relative to the centre of the small circle of the parallel on which they are located.

Angular distance = 123° - 67° = 56°

θ = 0°

R = 6400

π = $\frac{22}{7}$

Distance between U and V = $\frac{56}{360}$ x 2 x $\frac{22}{7}$ x 6400 x cos0

Distance between U and V = 6257.78 km ≈ 6258 km

(iii)

Latitude difference = 90°

Distance of U from the North pole = $\frac{90}{360}$ x 2 x $\frac{22}{7}$ x 6400

Distance of U from the North pole = 10057.14 km ≈ 10057 km

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