Angular Difference - SS3 Mathematics Lesson Note

The angle subtended at the center of the great or small circle by the minor arc formed by joining two places on the great or small circle respectively is known as the angular difference between the two places.

Note, for now, these angular differences involve places usually along the same latitude or same longitude.

ANGULAR DIFFERENCE ON THE SAME LONGITUDE

Example 1 Find the angular difference between the following pairs of places on the earth’s surface:

1. \(E(30{^\circ}N,\ \ 45{^\circ}E)\) and \(F(25{^\circ}S,\ 45{^\circ}E)\)

Solution

1. Points \(E\) and \(F\) are on the same longitude \(45{^\circ}E\), but, \(E\) is \(30{^\circ}N\) of the equator while \(F\) is \(25{^\circ}S\) of the equator, meaning they are on opposite sides of the equator and thus the difference between both points is \(30{^\circ} + 25{^\circ} = 55{^\circ}\).

ANGULAR DIFFERENCE ON THE SAME LATITUDE (ANGULAR DISTANCE)

Example 2 Find the angular difference between the following pairs of places on the earth’s surface:

1. \(A(40{^\circ}N,\ \ 35{^\circ}W)\) and \(B(40{^\circ}N,\ 50{^\circ}E)\)

Solution

1. Points \(A\) and \(B\) are on the same latitude \(40{^\circ}N\), but, \(A\) is on the \(35{^\circ}W\) meridian while \(B\) is on the \(50{^\circ}E\) meridian, meaning they are on opposite sides of the prime meridian and thus the difference between both points is \(35{^\circ} + 50{^\circ} = 85{^\circ}\).

Points \(C\) and \(D\) are on the same latitude \(30{^\circ}S\), but, \(C\) is on the \(20{^\circ}E\) meridian while \(D\) is on the 6\(0{^\circ}E\) meridian, meaning they are on the same side of the prime meridian and thus the difference between both points is \(60{^\circ} - 20{^\circ} = 40{^\circ}\).