Question

Calculate the distance between Lagos (4°N) and caire (30°N)

Answer 1

Using the Haversine formula:

d = 2r * arcsin( sqrt( sin^2((lat2-lat1)/2) + cos(lat1) * cos(lat2) * sin^2((lon2-lon1)/2) ) )

Where:
- d is the distance between the two points
- r is the radius of the Earth (mean radius = 6,371km)
- lat1 and lat2 are the latitudes of Lagos (4°N) and Cairo (30°N), respectively
- lon1 and lon2 are the longitudes of Lagos (assumed to be 0°) and Cairo (assumed to be 31°E), respectively

Substituting the values:

d = 2 * 6,371km * arcsin( sqrt( sin^2((30-4)/2) + cos(4) * cos(30) * sin^2((31-0)/2) ) )

d = 6,371km * arcsin( sqrt( sin^2(13) + 0.64 * sin^2(15.5) ) )

d = 6,371km * arcsin( sqrt( 0.0054 + 0.64 * 0.0315 ) )

d = 6,371km * arcsin( sqrt( 0.027 ) )

d = 6,371km * 0.283

d = 1,805km (rounded to the nearest km)

Therefore, the distance between Lagos and Cairo is approximately 1,805km.