A bearing is an angle measured clockwise from North, always written with three figures. Bearings problems are really trig problems in disguise: draw the North line at each point, mark the angles, then reach for right-angled trig, the sine rule or the cosine rule.
Always three figures, clockwise from North: due East is 090°, due South is 180°, and 7° is written 007°.
The bearing of A from B differs from the bearing of B from A by exactly 180°. Add 180° if the original is under 180°, otherwise subtract.
Draw a North line at each vertex. Use the fact that North lines are parallel — co-interior angles between them sum to 180° — to find the interior angle you need.
The bearing of C from A is 040°. Find the bearing of A from C.
A ship sails 30 km from P on a bearing of 070° to Q, then 40 km on a bearing of 160° to R. Find the direct distance PR.
The bearing of a lighthouse from a boat is 115°. Find the bearing of the boat from the lighthouse.
Point Q is due South of point P. Write down the bearing of Q from P.
The bearing of B from A is 250°. Find the bearing of A from B.
A boat sails 12 km on a bearing of 040°, then turns and sails 12 km on a bearing of 130°. Calculate the direct distance from start to finish.
From port A a ship sails 20 km on a bearing of 050° to B, then 35 km on a bearing of 110° to C. Calculate the distance AC.