Worked examples
The question
Question: B is east of A: find the bearing of B from A.
1 Draw the north line
A bearing starts at the north line.
It is measured clockwise, the way a clock turns, and written with 3 figures.
2 Measure clockwise
From north, turning clockwise to east: 90°.
East is a right angle from north: 90°.
With 3 figures: 090°.
bearing = 90° → 090°
Careful!
A bearing always has 3 figures.
We fill with zeros in front.
Careful: not 90° ✗
3 Check
Let's check: measured from north, clockwise, with 3 figures.
So it is right!
090°: from north, clockwise, 3 figures
Let's look back.
First: draw the north line.
Then: measure clockwise.
Last: check.
Answer Careful: not 90° ✗
▶ Watch it solved
The question
Question: the bearing of B from A is 065°: find the bearing of A from B.
1 Draw the north line
A bearing starts at the north line.
It is measured clockwise, the way a clock turns, and written with 3 figures.
At B we draw a north line too.
The two north lines are parallel.
2 Turn round
From B back to A is the opposite direction: half a turn more, 180°.
65 plus 180 is 245°.
back bearing = 065° + 180° = 245°
Why 180?
The north lines are parallel.
The angles between the path and the two north lines add up to 180°, as in the parallel lines lesson.
the north lines are parallel:
co-interior angles add to 180°
Careful!
A bearing is never negative.
Under 180°, we add 180.
Careful: not 65 − 180 = −115° ✗
3 Check
Let's check: the two bearings differ by exactly 180°, half a turn.
So it is right!
065° and 245° differ by 180°
Let's look back.
First: draw the north line.
Then: turn round.
Last: check.
Answer Careful: not 65 − 180 = −115° ✗
▶ Watch it solved
The question
Question: the bearing of B from A is 230°: find the bearing of A from B.
1 Draw the north line
A bearing starts at the north line.
It is measured clockwise, the way a clock turns, and written with 3 figures.
At B we draw a north line too.
The two north lines are parallel.
2 Turn round
From B back to A is the opposite direction: half a turn more, 180°.
230 is more than 180, so we take 180 away: 050°.
Adding would go past 360°.
back bearing = 230° − 180° = 050°
Why 180?
The north lines are parallel.
The angles between the path and the two north lines add up to 180°, as in the parallel lines lesson.
the north lines are parallel:
co-interior angles add to 180°
Careful!
A bearing is under 360°.
Over 180°, we take 180 away.
Careful: not 230 + 180 = 410° ✗
3 Check
Let's check: the two bearings differ by exactly 180°, half a turn.
So it is right!
230° and 050° differ by 180°
Let's look back.
First: draw the north line.
Then: turn round.
Last: check.
Answer Careful: not 230 + 180 = 410° ✗
▶ Watch it solved
