Question

The distance between two points A and B on latitude 60°S along their parallel of latitude is 2816km. Calculate the angular difference in their longitudes. If A is due west of B and on longitude 20°W, find the longitude of B

Answer 1

Part A

The angular difference of their longitude is approximately 50.65°

Part B

The location of B is on the longitude of approximately 30.65°E

Explanation:

Part A

The given parameters are;

The location of the points A and B = Along the parallel of latitude 60°

The radius of the Earth, R = 6,371 km

The radius at the 60° parallel of latitude, r = R × cos(θ)

∴ r = 6,371 × cos(60°) = 3,185.5

The circumference of the 60° parallel of latitude, C₆₀ = 2 × π × 3,185.5

The angle subtended by the arc formed by their distance apart, θ₁, is given as follows;

θ₁ = 2,816/(2 × π × 3,185.5) × 360 ≈ 50.65°

The angular difference of their longitude, θ₁ ≈ 50.65°

Part B

Given that the location of A is on the longitude 20°W and A is due west of B, we have the location of B is on the longitude (50.65° - 20°)E = 30.65°E

The location of B is on the longitude of approximately 30.65°E.