I hope you know vectors.

let the unit vector along East be

. and the unit vector along north be

.

The bearing is the direction specified from the North direction along the clockwise direction.

First leg of the travel: bearing of 075 for 11 km:

displacement vector is : 11 [ Cos(90-75)

* i *+ Sin (90-75)

*j *] km

second leg of the travel: bearing of 0 for 32 km:

displacement vector is: 32

* j * km

third leg of the travel is: 259 for 27 km.

angle between East & direction of travel: 259-90= 169 deg in clockwise direction.

displacement vector is: 27 (Cos (-169)

*i *+ Sin (-169)

*j *) km

Final displacement : sum of the three vectors;

= [11 Cos 15 + 27 Cos 169]

* i *+ [ 11 Sin 15 + 32 - 27 Sin 169 ]

* j * = -15.88

* i * + 29.69

*j * km

√(15.88² + 29.69²) = 33.67

Cos Ф = -15.88 / 33.67 = -0.4716

Sin Ф = 29.69 / 33.67

Ф = 118.14° from East anti clockwise. So 18 deg from North.

final position:

So bearing of the ship from the port is 360 - 18 = 342 from north.

So bearing of the port from the ship is : 180 - 18= 162 from north.

Distance from the port: 33.67 km.