A ship sails from port A to port B, 30 km away on a bearing of 060^. It then sails to port C, 40 km away on a bearing of 150^. Find the distance between port A and port C.

Let's solve this bearing problem step-by-step.

Part (i): Calculate the distance between city B and city C to two decimal places.

Step 1: Determine the angle $\angle CAB$.
The bearing of B from A is $150^\circ$.
The bearing of A from C is $015^\circ$. To find the bearing of C from A, we add $180^\circ$ to the bearing of A from C because $015^\circ < 180^\circ$.
Bearing of C from A $= 015^\circ + 180^\circ = 195^\circ$.
The angle $\angle CAB$ is the difference between the bearing of C from A and the bearing of