Sketch the situation and determine the angles in the triangle formed by the port (P) and the positions of ships A and B after one hour (A' and B').

To find the speed of ship B, we need to use trigonometry based on the given bearings and distances.

Step 1: Sketch the situation and determine the angles in the triangle formed by the port (P) and the positions of ships A and B after one hour (A' and B').
Let P be the port.
After 1 hour:

• Ship A is at A'. Distance $PA' = \text{Speed of A} \times \text{Time} = 10 \text{ km/h} \times 1 \text{ h} = 10 \text{ km}$.
• Ship B is at B'. Distance $PB' = \text{Speed of B} \times \text{Time} = \text{Speed of B} \times 1 \text{ h}$. Let $PB' = x$ km.

The bearings are measured clockwise from the North line.

• Bearing of A from P is $104^\circ$.
• Bearing of B from P is $160^\circ$.

The angle $\angle A'PB'$ (the angle at the port P) is the difference between these two bearings:

$$\angle A'PB' = 160^\circ - 104^\circ = 56^\circ$$

Step 2: Determine the angle $\angle PA'B'$ (the angle at A').
Draw a North line at P and a parallel North line at A'.

• The bearing of A' from P is $104^\circ$.
• The back bearing of P from A' is $104^\circ + 180^\circ = 284^\circ$. This is the angle from the North line at A', clockwise to the line A'P.
• The bearing of B' from A' is given as $215^\circ$. This is the angle from the North line at A', clockwise to the line A'B'.

The angle $\angle PA'B'$ is the difference between the bearing of P from A' and the bearing of B' from A':

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