Convert the latitude of A to decimal degrees.

1. An aeroplane flies from a point A ($1^\circ 15'S, 37^\circ E$) to a point B directly North of A. AB subtends an angle of $45^\circ$ at the centre of the earth. From B, the aeroplane flies to a point C on longitude $23^\circ W$. (Take the value of $\pi$ as $\frac{22}{7}$ and radius of the earth as 6370 km).

a) (i) Find the latitude of B.

Step 1: Convert the latitude of A to decimal degrees.
$1^\circ 15'S = 1 + \frac{15}{60}^\circ S = 1.2