True bearings
Read true bearings as three-figure angles measured clockwise from north, find back-bearings, and solve bearing problems.
Worked examples
Reading a true bearing from a diagram
Straightforward
Problem
A compass diagram has north pointing straight up. A direction is marked clockwise from north. Write this direction as a true bearing.
1
Recall the definition of a true bearing.
A true bearing is the angle measured clockwise from north to the direction. It is always written as a three-figure number, e.g. , , .
2
Read the angle from the diagram.
The diagram shows the direction is clockwise from north.
3
Write the true bearing.
The true bearing is . Since it already has three figures, no leading zero is needed.
Answer
The true bearing is .
True bearing of an intercardinal direction
Moderate
Problem
State the true bearing of south-west (SW) and explain where it appears on a compass diagram.
1
Identify the bearings of the adjacent cardinal directions.
South and West .
2
Find the midpoint between south and west.
3
Describe the position on a compass diagram.
On a diagram with north pointing up, the SW direction points down and to the left. It is clockwise from north — halfway between the south and west arms of the compass.
Answer
The true bearing of south-west is .
Finding a back-bearing
Challenging
Problem
A ship sails from port P on a true bearing of and arrives at port Q. The captain then needs to sail directly back to P. What bearing must the captain use for the return journey?
1
State the back-bearing rule.
The bearing from B to A is always exactly different from the bearing from A to B, because the directions are opposite. Add if the forward bearing is less than ; subtract if it is or more.
2
Determine which case applies.
The bearing from P to Q is . Since , add .
3
Calculate the back-bearing.
4
Check the answer is reasonable.
PQ points north-east ( is between and ), so QP should point south-west. A bearing of lies between and (the SW sector) — this is consistent.
Answer
The captain must sail on a bearing of to return to P.
Practise
Q1·Straightforward
A compass diagram has north pointing straight up. A direction is marked clockwise from north. What is the true bearing of this direction?
Explanation
True bearings are measured clockwise from north. Since the direction is clockwise from north, the true bearing is .
Q2·Straightforward
What is the true bearing of due east?
Explanation
Starting from north () and turning clockwise, a quarter turn reaches east. , so the true bearing of east is .
Q3·Straightforward
A compass diagram shows a direction pointing exactly south. What is the true bearing?
Explanation
Starting from north () and turning clockwise, a half-turn reaches south. , so the true bearing of south is .
Q4·Straightforward
A diagram shows a direction clockwise from north. What is the true bearing?
Explanation
True bearings are the clockwise angle from north to the direction. The direction is clockwise from north, so the true bearing is .
Q5·Moderate
What is the true bearing of south-east (SE)?
Explanation
East is and south is . South-east lies midway between them: . The true bearing of SE is .
Q6·Moderate
What is the true bearing of north-west (NW)?
Explanation
West is and north is (equivalent to ). North-west lies midway: . The true bearing of NW is .
Q7·Moderate
A compass diagram shows a direction on a true bearing of . In which sector does this direction fall?
Explanation
The four cardinal directions divide the compass into sectors: NE (–), SE (–), SW (–) and NW (–). Since , the direction falls in the north-west sector.
Q8·Moderate
A compass diagram shows a direction on a true bearing of . How many degrees from south () is this direction?
Explanation
. The direction at is short of south, so it is away from the south direction on the compass.
Q9·Challenging
The bearing from A to B is . What is the bearing from B to A (the back-bearing)?
Explanation
Since , the back-bearing . The rule is: add if the forward bearing is less than ; subtract if it is or more. This keeps the back-bearing between and .
Q10·Challenging
The bearing from P to Q is . What is the bearing from Q to P?
Explanation
, so the back-bearing . The direction PQ points south-east, so the reverse direction QP points north-west — and (between and ) confirms this.
Q11·Challenging
The bearing from X to Y is . What is the bearing from Y to X?
Explanation
, so the back-bearing . The direction XY points south-west, so the reverse direction YX points north-east — and (between and ) confirms this.
Q12·Challenging
Town B is on a true bearing of from town A. A traveller walks from A to B, then turns to walk directly back to A. What true bearing must they walk on the return journey?
Explanation
, so the back-bearing . The traveller must walk on a bearing of to return to A. The direction AB points north-west (), so BA points south-east ().