Bearings

• M is due north of L.
• The bearing of K from M is 234°.

Calculate the bearing of K from L.

It then turns and sails 70 km to C.

Finally, it sails 85 km back to A.

Calculate the bearing of A from C.

They stand back-to-back and then walk in different straight-line directions from the same starting point.

Alan walks 2.3 metres on a bearing of 60°. Claire walks 3.8 metres on a bearing of 110°.

How far apart are Alan and Claire now?

In a race, boats sail round three buoys represented by A, B, and C in the diagram below.

B is 8 kilometres from A on a bearing of 060°.
C is 11 kilometres from B.
A is 13 kilometres from C.

(a)  Calculate the size of angle ABC.

(b)  Hence find the size of the shaded angle.

In the diagram below P, Q and R represent the positions of Portlee, Queenstown and Rushton respectively.

Portlee is 25 kilometres due South of Queenstown.
From Portlee, the bearing of Rushton is 072°.
From Queenstown, the bearing of Rushton is 128°.
Calculate the distance between Portlee and Rushton.
Do not use a scale drawing.

In the diagram below D, E and F represent the positions of Dunbridge, Earlsford and Fairtown respectively.
Dunbridge is 15 km west of Earlsford.
From Dunbridge, the bearing of Fairtown is $\displaystyle 126^{\circ}.$
From Earlsford the bearing of Fairtown is $\displaystyle 230^{\circ}.$

Calculate the distance between Dunbridge and Fairtown.

A ferry and a trawler receive a request for help from a stranded yacht.
On the diagram the points F, T and Y show the positions of the ferry, the trawler and the yacht respectively.

• FY is 7.2 kilometres.
• TY is 5.6 kilometres.
• FT is 10.3 kilometres.
• F is on a bearing of $\displaystyle 240^{\circ}$ from T.
Calculate the bearing of the yacht from the trawler.

A fishing boat and a yacht left a harbour at the point H.

The fishing boat travelled 3.4 kilometres on a bearing of 047° to the point F.

The yacht travelled 5.7 kilometres on a bearing of 115° to the point Y.

Calculate the distance between the fishing boat at F and the yacht at Y.

In the diagram A, B and C represent the positions of three checkpoints in an orienteering course.

• B is 250 metres east of A.
• The bearing of C from A is 131°.
• C is 200 metres from B.
Calculate the bearing of C from B.