GCSE Maths · Geometry and measures

Bearings GCSE Questions, Worked Examples and Answers

A bearing is a direction measured clockwise from north and written with three figures. The point after “from” is where the angle must be measured, so place the north line there before calculating or measuring.

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Measure from the starting point

What you need to know about GCSE bearings

A bearing tells you the direction of one point from another. Imagine standing at the starting point and facing north: turn clockwise until you face the destination. The size of that turn is the bearing, written with three figures such as 065°.

North → clockwise → three figures

Read the wording before the angle

For the bearing of B from A, the journey begins at A. That decides where the north line and angle belong.

Starting pointfrom Aput the north line at A

Directionclockwiseturn from north towards AB

Write065°use exactly three figures

The bearing of B from A is 065°. Start at A, draw or identify north at A, then turn clockwise to the route AB.

Put this compass cross at the point after “from”. Choose the destination quadrant before calculating so your final bearing has a sensible size.

If B is on a bearing of 065° from A, reversing the route turns through 180°, so A is on a bearing of 245° from B. Parallel north lines let you justify the same result with angle facts.

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Measure or draw a bearing

What the problem asks: A scale diagram is given, or the question asks you to draw a direction.

How to solve it: Put the protractor centre at the stated starting point, align zero with north and measure clockwise.

Find a reverse bearing

What the problem asks: You know the bearing of B from A and need A from B.

How to solve it: Reverse the direction by adding 180° when the bearing is below 180°, or subtracting 180° when it is at least 180°.

Use angle facts

What the problem asks: North lines appear at two or more points and another angle is given.

How to solve it: Treat north lines as parallel and use alternate, corresponding, co-interior or angles-around-a-point facts. This also explains why a reverse bearing differs by 180°.

Calculate from distances

What the problem asks: The north/south and east/west movements form a right-angled triangle.

How to solve it: Find the acute angle θ first. Convert by quadrant: NE θ, SE 180° − θ, SW 180° + θ, NW 360° − θ.

A reliable routine

Routine for every bearings diagram

Use this routine when a question asks you to read, measure, draw or calculate a bearing.

Underline the direction phrase and identify the point after ‘from’.
Draw or mark north at that starting point.
Trace clockwise from north to the destination line and calculate or measure that angle.
Write the final angle with three figures and a degree sign.

Check: A quick sketch should show the bearing in the same quadrant as the destination. For example, a south-west direction cannot have a bearing below 180°.

Fully worked

Bearings GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Write a three-figure bearing

1 mark

Question

A direction is $72^\circ$ clockwise from north. Write it as a bearing.

A bearing needs three figures. Add a leading zero.

$\boxed{072^\circ}$

Example 2

Find a reverse bearing

2 marks

Question

The bearing of B from A is $062^\circ$ . Find the bearing of A from B.

The reverse direction is half a turn, or $180^\circ$ , further round.

$062^\circ+180^\circ=242^\circ$

$\boxed{242^\circ}$

Example 3

Reverse a bearing above 180 degrees

2 marks

Question

The bearing of a lighthouse from a boat is $218^\circ$ . Find the bearing of the boat from the lighthouse.

Because $218^\circ$ is above $180^\circ$ , subtract $180^\circ$ .

$218^\circ-180^\circ=38^\circ$

Write the answer using three figures.

$\boxed{038^\circ}$

Example 4

Use an angle at a north line

3 marks

Question

C is south-east of B. The angle between the east direction from B and the line BC is $34^\circ$ . Find the bearing of C from B.

East has bearing $090^\circ$ . The route is another $34^\circ$ clockwise towards south.

$090^\circ+34^\circ=124^\circ$

$\boxed{124^\circ}$

Example 5

Calculate a bearing from two movements

Harder4 marks

Question

Point Q is $9$ km east and $12$ km north of P. Calculate the bearing of Q from P to the nearest degree.

The route is north-east. Let $\theta$ be the clockwise angle from north.

Relative to $\theta$ , east is opposite and north is adjacent.

$\tan\theta=\frac{9}{12}$

$\theta=\tan^{-1}\left(\frac{9}{12}\right)$

$\theta=36.87\ldots^\circ$

$\boxed{037^\circ}$

Example 6

Resolve a journey into east and south distances

Harder5 marks

Question

A boat travels $25$ km on a bearing of $130^\circ$ . Calculate how far east and how far south it travels. Give each answer to 1 decimal place.

The route is in the south-east quadrant. The acute angle between the route and south is

$180^\circ-130^\circ=50^\circ$

In the right-angled triangle, east is opposite $50^\circ$ .

$\text{east}=25\sin50^\circ$

$\text{east}=19.151\ldots$

South is adjacent to $50^\circ$ .

$\text{south}=25\cos50^\circ$

$\text{south}=16.069\ldots$

$\boxed{19.2\text{ km east and }16.1\text{ km south}}$

Example 7

Use parallel north lines

3 marks

Question

The bearing of B from A is $065^\circ$ . Use the parallel north lines to find the bearing of A from B.

If B is on a bearing of 065° from A, reversing the route turns through 180°, so A is on a bearing of 245° from B. Parallel north lines let you justify the same result with angle facts.

The route from B to A is the opposite direction along the same straight line. A half-turn is $180^\circ$ .

$065^\circ+180^\circ=245^\circ$

This agrees with the angle facts formed by the two parallel north lines.

$\boxed{245^\circ}$

Example 8

Locate a point using two bearings

4 marks

Question

A and B are $10$ cm apart on an east–west line. Draw a ray from A on a bearing of $045^\circ$ and a ray from B on a bearing of $315^\circ$ . Label their intersection C and measure AC.

The two measured rays meet at C. In a scale drawing, C is the point satisfying both given bearings.

Draw a north line at A and measure $45^\circ$ clockwise. Draw a north line at B and measure $315^\circ$ clockwise.

The rays meet directly above the midpoint of AB, so the horizontal and vertical movements from A are both $5$ cm.

$AC=\sqrt{5^2+5^2}$

$AC=\sqrt{50}=7.071\ldots$

$\boxed{AC\approx7.1\text{ cm}}$

Exam tip: keep both north lines parallel and extend each ray far enough to intersect.

15 original questions · total 51 marks

Bearings GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 60 minutes · sketch north and the destination quadrant before calculating · answers start collapsed

Format a small bearing

1 mark

Write $8^\circ$ clockwise from north as a bearing.

Show worked answer

Use three figures: $\boxed{008^\circ}$ .

Recognise a compass direction

1 mark

State the bearing for a journey due west.

Show worked answer

West is three quarters of a full clockwise turn from north.

$\boxed{270^\circ}$

Use parallel north lines

3 marks

The bearing of B from A is $065^\circ$ . Find the reverse bearing and explain why the two bearings differ by $180^\circ$ .

If B is on a bearing of 065° from A, reversing the route turns through 180°, so A is on a bearing of 245° from B. Parallel north lines let you justify the same result with angle facts.

Show worked answer

North lines at A and B are parallel, and AB is a transversal. The route BA continues in the opposite direction along the same straight line, so its clockwise direction is half a turn later.

$065^\circ+180^\circ=245^\circ$

$\boxed{245^\circ}$

Construct two bearings

4 marks

A and B are $10$ cm apart on an east–west line. C is on a bearing of $045^\circ$ from A and $315^\circ$ from B. Construct C and measure AC.

The two measured rays meet at C. In a scale drawing, C is the point satisfying both given bearings.

Show worked answer

Draw the two north lines parallel. Measure each bearing clockwise and extend the rays until they meet at C.

The construction gives

$\boxed{AC\approx7.1\text{ cm}}$

Allow a small measurement tolerance for an accurately drawn scale diagram.

Use an angle from east

3 marks

A path is $27^\circ$ north of east. Find its bearing.

Show worked answer

East is $090^\circ$ . Moving $27^\circ$ towards north makes the clockwise angle smaller.

$090^\circ-27^\circ=63^\circ$

$\boxed{063^\circ}$

Use an angle from south

4 marks

A ship sails $38^\circ$ west of south. Find its bearing.

Show worked answer

South is $180^\circ$ . Turning from south towards west increases the clockwise angle.

$180^\circ+38^\circ=218^\circ$

$\boxed{218^\circ}$

Calculate a north-east bearing

Harder4 marks

R is $15$ km north and $8$ km east of S. Calculate the bearing of R from S to the nearest degree.

Show worked answer

Let $\theta$ be the angle clockwise from north.

$\tan\theta=\frac{8}{15}$

$\theta=28.07\ldots^\circ$

$\boxed{028^\circ}$

Calculate a south-east bearing

Harder4 marks

T is $7$ km east and $5$ km south of U. Calculate the bearing of T from U to the nearest degree.

Show worked answer

First find the acute angle east of south.

$\tan\alpha=\frac{7}{5}$

$\alpha=54.46\ldots^\circ$

The bearing from north is $180^\circ-\alpha$ .

$180^\circ-54.46\ldots^\circ=125.53\ldots^\circ$

$\boxed{126^\circ}$

Find a distance north

Harder5 marks

A walker travels $18$ km on a bearing of $040^\circ$ . Calculate the distance travelled north, to 1 decimal place.

Show worked answer

The north distance is adjacent to the $40^\circ$ angle.

$\text{north}=18\cos40^\circ$

$=13.788\ldots$

$\boxed{13.8\text{ km}}$

Find a bearing from coordinates

Harder5 marks

On a map, A has coordinates $(2,3)$ and B has coordinates $(-4,11)$ . North is the positive y-direction. Calculate the bearing of B from A to the nearest degree.

Show worked answer

From A to B, the movement is $6$ units west and $8$ units north.

Find the acute angle west of north.

$\tan\alpha=\frac{6}{8}$

$\alpha=36.87\ldots^\circ$

The clockwise bearing is $360^\circ-\alpha$ .

$360^\circ-36.87\ldots^\circ=323.13\ldots^\circ$

$\boxed{323^\circ}$

Convert an anticlockwise angle

2 marks

A route is $40^\circ$ anticlockwise from north. Write its bearing.

Show worked answer

Bearings must be measured clockwise. Complete the full turn.

$360^\circ-40^\circ=320^\circ$

$\boxed{320^\circ}$

Use an angle at the destination

4 marks

The bearing of Q from P is $072^\circ$ . At Q, turn clockwise from QP through $46^\circ$ to face R. Find the bearing of R from Q.

Show worked answer

First reverse the given bearing.

$072^\circ+180^\circ=252^\circ$

Now turn clockwise through $46^\circ$ .

$252^\circ+46^\circ=298^\circ$

$\boxed{298^\circ}$

Resolve a south-west journey

Harder4 marks

A hiker walks $12$ km on a bearing of $215^\circ$ . Find the west and south components to 1 decimal place.

Show worked answer

The acute angle west of south is

$215^\circ-180^\circ=35^\circ$

$\text{west}=12\sin35^\circ=6.882\ldots$

$\text{south}=12\cos35^\circ=9.830\ldots$

$\boxed{6.9\text{ km west and }9.8\text{ km south}}$

Calculate a south-east bearing from coordinates

Harder5 marks

C is at $(-3,2)$ and D is at $(5,-4)$ . North is the positive y-direction. Find the bearing of D from C to the nearest degree.

Show worked answer

From C to D, move $8$ units east and $6$ units south, so the route is south-east.

Let $\alpha$ be the acute angle east of south.

$\tan\alpha=\frac{8}{6}$

$\alpha=53.13\ldots^\circ$

$\text{bearing}=180^\circ-53.13\ldots^\circ$

$\boxed{127^\circ}$

Check a reverse bearing stays below 360 degrees

2 marks

The bearing of a tower from a gate is $256^\circ$ . Find the bearing of the gate from the tower.

Show worked answer

Adding $180^\circ$ gives $436^\circ$ , which is beyond one full turn. Subtract $360^\circ$ .

$436^\circ-360^\circ=76^\circ$

Write three figures.

$\boxed{076^\circ}$

Examiner-style feedback

Common bearings mistakes

Measuring from the wrong point

In ‘the bearing of B from A’, measure at A. The word after ‘from’ identifies the start.

Turning anticlockwise

Bearings are measured clockwise from north, even when an anticlockwise angle looks smaller.

Reading 040° instead of 320°

If the route is 40° anticlockwise from north, the clockwise bearing is 360° − 40° = 320°. Trace the clockwise arc before writing the number.

Leaving a reverse bearing above 360°

If adding 180° gives a result such as 436°, subtract 360° to return to one full turn: 076°.

Writing two figures

Write 65° as 065°. A correct bearing always has three figures.

Trusting an inaccurate sketch

Use the diagram to choose the quadrant, but use stated values and angle facts for the calculation unless told to measure.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Start at the point named after ‘from’.
Mark north at that point.
Turn clockwise to the destination line.
Check the quadrant and write three figures.

Quick answers

Bearings FAQ

Are bearings measured clockwise or anticlockwise?

Always clockwise from north.

Why do bearings have three figures?

The three-figure convention makes directions unambiguous, so 7° is written 007° and 65° as 065°.

How do I find a reverse bearing?

Add or subtract 180° so the result remains between 000° and 360°.

Can a bearings question use trigonometry?

Yes. Distances often create a right-angled triangle, so you may need sine, cosine or tangent before converting the angle to a bearing.

Build connected skills

What to revise next

Right triangles

Trigonometry

Calculate missing sides and angles inside bearing problems.

Revise trigonometry

Directed movement

Vectors

Represent routes using horizontal and vertical displacement.

Revise vectors

Accurate calculation

Standard form

Keep very large navigation distances manageable.

Revise standard form

Content standards

Curriculum and rights review

Curriculum references checked 4 September 2026. Measuring, drawing and calculating bearings is shared GCSE Mathematics content. The questions, diagrams, values and solution wording are original Pass an Exam material.

Official specification references