Read and use three-figure bearings
Measure and write three-figure bearings from a declared north line, reverse route directions and distinguish a waypoint’s interior angle from a heading change.
Section 4.4 · Measures
Exam scope and assessment notes
Foundation and Higher share the seven published F:4.4A–G Measures rows. The Higher table says See Foundation Tier; there are no additional H4.4 rows. The chosen eight-lesson split covers instrument scales, time intervals, estimates, nearest-degree angle measurement, three-figure bearings, average speed, density and pressure. Eight lessons and thirty-two original worked/staged cases are StudyForA’s design, not a syllabus-prescribed count. Each structural source link requires the corresponding complete teaching record carrying that source ID, a worked explanation and all Guided, Independent and Transfer stages. F4.4F requires the complete speed lesson; broad F4.4G requires all three speed, density and pressure lessons, not a speed-only partial link. Source binding and substantive structure must belong to the same record; a separate untagged duplicate cannot supply missing evidence. These are structural links, not exhaustive subskill or specialist approval. Preserve the actual calibrated instrument ticks, pointer/meniscus positions, ruler endpoints, units and protractor alignment action. Read labelled scales rather than assuming CSS pixels are millimetres. Use only diagrams explicitly supplied as accurate for measurement; ordinary examination diagrams need not be to scale and must not be measured without instructions. Numerical reference readings, protractor openings and the measured bearing remain hidden before a calibrated learner attempt; revealing a reference is not proof of instrument operation. Keep ideal model values separate from approximate human readings and nearest-degree rounding; no universal automatic tolerance or measurement competence is established. Bearings start at the named origin and run clockwise from declared north, with parallel north assumptions stated and leading zeros retained. Distinguish reverse rays, interior route angles and forward heading changes; no magnetic or globe-navigation correction is inferred. Clock intervals retain am/pm, noon/midnight and day order. Average speed uses total route distance over the full named elapsed interval, including stated stops; displacement and instantaneous speed are different. Calculating time by division requires positive speed: at constant zero speed a positive distance is impossible, while zero distance alone does not determine elapsed time. Keep density mass/volume units compatible and volume positive; liquid displacement is final minus initial level. Combined volumes are added only under the stated no-void/no-volume-change assumption. The pressure formula is supplied in every pressure stage; do not infer that the density or average-speed formula is also supplied. Use a provided force in newtons, positive contact area, correct squared-area conversion and an explicitly limited average-pressure model. No real-world safety or route-feasibility certification follows. The source assessment context uses SI units and may require mathematical instruments. These lessons do not complete4.5 nearest-mm line drawing, formal shape/compass constructions or scale-drawing problems,5.2 transformations,4.8 bearing trigonometry,4.9/4.10 full mensuration or4.11 map/similarity work. No blanket formal-proof waiver is imported. Written practice is self-checked, not automatically marked; acknowledgements and attempts do not award marks or establish mastery. Specialist approval and formal assessment validation remain unestablished. Publisher navigation is separate evidence: literal F4.4D appears in Book2 Shape and Space6, map physical10/pages128–160, and Hub36 Bearings and Scale Drawings, co-tagged F4.5C/F4.11B; those co-tags confer no construction/map credit here. Literal F4.4G appears in Book1 Number5, map physical5/pages255–268, and Hub13 Compound Measures. A/B/C/E/F have no literal4.4 chapter or Hub tag in that map; do not invent one from nearby time or scale-drawing topics. Book1 public uncorrected-proof contents start Number5/Compound measures at256 and end its summary at269, conflicting with map255–268; preserve both references. Book2 chapter start128 and next start161 agree with its map range, but no explicit bearings contents heading locates every skill. Neither relevant chapter body is present in the public samples. Full final-book/Teaching Hub content and pagination alignment remain unverified; chapter links are not full-book or modular teaching credit. The current2026/2027 manual lists linear4MA1 F/H in November2026 and June2027; FR/HR are June2027 only, based on centre eligibility. Vietnam is on the regional-centre list; learner residence alone does not choose an option. The table points to page2 although the list is on physical/printed3. Modular4XMAF/4XMAH cash-ins and4WM units remain separate entries for international centres. This entry context does not create a2027 revision of the Issue2 specification.
Before you begin
- Measure or reason about angles in degrees and recognise a full 360° turn.
- Use straight-line and parallel-line angle relationships.
- Distinguish ray AB from reverse ray BA in a labelled route.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
The bearing of B from A is measured from which ray and in which direction?
What you will learn
- Name the observation point and measure clockwise from its north line.
- Use leading zeros and reverse a bearing by 180° with parallel north lines.
- Draw and reason about a two-stage route without confusing heading change with the angle back to the previous point.
Use the accurate supplied diagram with A as the origin, a declared north ray at A and the route ray AB towards the northeast. Its bearing value is not printed for you. Measure clockwise from north and write the bearing of B from A with three figures. With parallel north at B, find the reverse bearing of A from B and the small angle from east towards AB. Measure before opening the numerical reference.
Read, draw and calculate before comparing. Every requested part and explanation needs your own attempt. The teal protractor and orange rays show your actual placements, including wrong ones. Comparisons do not award marks or establish practical instrument competence.
Coordinates use the original worksheet grid. The entire drawing and your tools rotate together; clockwise bearings retain their direction. Case or orientation changes clear all responses, placements and references. Named given points can be placed exactly; other drawing clicks use the nearest half-unit grid point and never snap to a solution.
Given panel 1
The board retains the last submitted valid placement. Editing a draft invalidates its submission without moving the last drawing; submit again before comparison.
A bearing starts at a named point and at north
The bearing of B from A starts at A, where you stand or observe. Draw or identify the declared north line at A, then turn clockwise from north to the ray AB. Write the result with three figures: north is 000°, east 090°, south 180° and west 270°. The leading zeros in 042° or 009° are part of the convention, not a different angular size.
North must be supplied or declared; it is not automatically the top edge of a page that may have been turned. When a diagram is explicitly accurate, a protractor can measure its bearing from the north ray, using the clockwise sweep. A west-of-north direction may have a large clockwise bearing even though the short angle beside north is small. These tasks do not introduce magnetic declination or globe-navigation corrections.
Reverse a route with parallel north lines
At B, draw the north line parallel to the one at A, as assumed in these local route diagrams. The reverse ray BA points opposite AB, so its bearing differs by 180°. Add 180° when the original bearing is below 180°, or subtract 180° when it is at least 180°, then express the result between 000° and just under 360°.
Name both directions before using the rule: “B from A” and “A from B” are not interchangeable. Draw their clockwise north arcs at their different origins. For a southwest direction, compare the given bearing with 180° to describe its angle west of south; then reverse the route to find its northeast bearing. The rule relies on the stated parallel north lines, not on treating the two origins as one point.
Separate an interior angle from a course change
For a journey A→B→C, the incoming heading is the direction of AB, continued forward through B. The interior angle ∠ABC instead uses BA, the ray back towards A, and BC, the ray onwards to C. Reverse AB first when you need that interior angle. A clockwise course change compares the incoming forward heading with the outgoing heading, wrapping through 000° if necessary.
Draw the north lines and label the given bearings before calculating. Use the angle between the correct rays and explain the reversal or full-turn subtraction. A rough sketch helps organise this calculation without claiming a scale drawing or a formal triangle construction. Distances that would require trigonometry or a measured map scale belong to other requirements and are not inferred from this bearing lesson.
Sources for this lesson
Pause and explain
An incoming heading is 285° and the outgoing heading is 014°. What is the clockwise course change?
Worked example
Use the accurate supplied diagram with A as the origin, a declared north ray at A and the route ray AB towards the northeast. Its bearing value is not printed for you. Measure clockwise from north and write the bearing of B from A with three figures. With parallel north at B, find the reverse bearing of A from B and the small angle from east towards AB. Measure before opening the numerical reference.
Show the worked solution
- At A, start on the declared north ray, then measure the clockwise sweep to AB. The private diagram’s ideal bearing is 68°, so write the nearest-degree reference as 068°.
- At B, the north line is parallel to north at A. BA is opposite AB, so add 180°: 68+180=248°. This is the bearing of A from B, not the original forward direction.
- East has bearing 090°. AB lies between north and east, so the small angle from east back towards AB is 90−68=22°.
- Keep the two observation points and angle arcs labelled. The measured forward reference is about 068°; the reverse and east relation follow from the same ideal reference and the parallel-north assumption.
Answer Forward reference bearing: 068°. Reverse bearing: 248°. Small angle from east towards AB: 22°.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
B lies on a bearing of 215° from A. Sketch A, its declared north line and the southwest route ray AB; mark the given clockwise bearing. With parallel north at B, draw the reverse ray and find its bearing. Describe AB as a number of degrees west of south. Explain rather than measuring a rough sketch for an exact result.
Give me a hint
South is 180°. Reversing a direction changes its bearing by 180°.
Compare my reasoning
- Start at A and turn clockwise from north through 180° to south, then another 215−180=35° towards west. Sketch AB in that southwest direction.
- At B draw north parallel to north at A. The reverse ray BA points northeast, opposite AB.
- Subtract 180° from 215° to get the reverse bearing 35°. Write it as 035° using three figures.
- AB is 35° west of south. The given exact bearing and angle relationships justify these numbers; a rough sketch only organises the reasoning.
Reverse bearing: 035°. AB is 35° west of south.
Look for these in your work
- Draw north at both named origins and mark the clockwise given bearing.
- Reverse 215° to 035° with the leading zero.
- Explain the 35° west-of-south direction without claiming formal construction accuracy.
A→B has bearing 312° and B→C has bearing 047°, with parallel north lines. Use the labelled route diagram and draw north at the relevant origins. Independently find the bearing of A from B, the smaller ∠ABC and the clockwise change from incoming heading AB to outgoing heading BC. Show which two rays form each requested angle.
Give me a hint
For ∠ABC use BA, not the incoming forward heading. A clockwise heading change may pass through 000°.
Compare my reasoning
- Reverse AB: 312−180=132°, so the bearing of A from B is 132°. At B this identifies the ray BA back towards A.
- The ray BC has bearing 047°. The smaller angle between BA at 132° and BC at 47° is 132−47=85°, giving ∠ABC.
- The incoming forward heading remains 312°, while the outgoing heading is 047°. A clockwise turn passes through north: (360−312)+47=48+47=95°.
- Label 85° inside the route angle at B and 95° on the heading-change arc. They use opposite versions of the incoming direction, so they answer different questions.
Bearing of A from B: 132°. Smaller ∠ABC: 85°. Clockwise course change: 95°.
Look for these in your work
- Draw and use parallel north lines and the given three-figure bearings.
- Use BA=132° to obtain the 85° interior angle.
- Explain the 95° clockwise heading change separately from ∠ABC.
A→B has bearing 075° and B→C has bearing 140°. Draw and label parallel north lines in the route diagram. Find both reverse bearings, the smaller ∠ABC and the clockwise change from the incoming AB heading to the outgoing BC heading. Explain why the last two angles differ. No route lengths or map scale are supplied.
Give me a hint
Reverse each route direction before finding its reverse bearing, but compare forward headings for a course change.
Compare my reasoning
- Reverse AB by adding 180°: 75+180=255°. Thus the bearing of A from B is 255°.
- Reverse BC similarly: 140+180=320°. Thus the bearing of B from C is 320°.
- At B, the rays BA and BC have bearings 255° and 140°. Their smaller separation is 255−140=115°, so ∠ABC=115°.
- The forward headings change clockwise from 075° to 140° by 140−75=65°. The interior angle uses BA, whereas the heading change uses AB continued forward; 115° and 65° are supplements here.
Reverse bearings: 255° and 320°. Smaller ∠ABC=115°. Clockwise course change=65°, using a different incoming ray.
Look for these in your work
- Give both reverse bearings with correct origins.
- Show that ∠ABC uses BA and gives 115°.
- Distinguish the 65° course change and avoid inventing distance or scale information.
Common mistakes
- Starting at the destination or measuring anticlockwise from north without converting to the clockwise bearing.
- Omitting leading zeros, or assuming the top of a rotated page is north.
- Using the incoming heading instead of the reverse ray when finding an interior waypoint angle.
What can you explain now?
A→B has bearing 300°. What is the bearing of A from B when the two north lines are parallel?
Compare with the explanation
120°.
The reversed ray differs by 180°. Subtract 180 from 300 to keep the bearing within one full turn: 300−180=120°.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
State the origin, declared north ray, clockwise direction and three-figure format. Then explain why reversing a ray changes the bearing by 180° and why a route interior angle differs from a forward heading change.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.