A bearing is a direction, not a length
A school map asks you to travel from one checkpoint to another. The map shows several long paths, north arrows and a triangle. It is tempting to measure whatever angle looks obvious and call it a bearing. That is the mistake this guide repairs. A bearing describes horizontal direction, conventionally measured clockwise from north. It is written as a three-figure angle, such as 045°, 120° or 300°. The straight-line distance between two points is a different quantity. An accurate bearing answer begins by identifying the point from which the direction is observed. Only then should you draw the north reference and choose a trigonometric calculation.
Match the correct 2027 examination, not an older code
The official 2027 G3 Singapore-Cambridge Secondary Education Certificate Mathematics syllabus is K310; the SEAB register shows 4052 as the earlier reference code. The K310 content explicitly includes two- and three-dimensional problems involving bearings, angles of elevation and depression, as well as the sine and cosine rules and right-triangle trigonometry. Mathematics has two written papers, each lasting 2 hours 15 minutes, carrying 90 marks and contributing 50 per cent. Paper 2 has longer problems and a final question applying Mathematics to a real-world situation. The published syllabus states conventions for rounding non-exact answers when a question does not specify another accuracy. This guide teaches bearing reasoning, not a claim that a particular route will appear in a future paper. Verify the current details through the SEAB 2027 G3 subject register and K310 Mathematics syllabus.
North belongs to the observing point
Imagine points A and B on a map. A bearing of B from A uses a north line drawn through A, because A is the starting point. A bearing of A from B uses a north line drawn through B, because B is now the starting point. If you draw the reference at the wrong vertex, even a perfect angle calculation can answer the wrong question. The phrase ‘bearing of B from A’ should be translated into an arrow starting at A and pointing toward B. Mark the starting point first. Mark north second. Draw the directed segment third. At that stage, the bearing becomes a well-defined angle rather than a guess from the picture.
Clockwise is an instruction, not a preference
Turn from north towards east: that is 090°. Turn from north towards south: 180°. Turn towards west: 270°. Return to north: a complete clockwise rotation is 360°, which corresponds to a direction also represented by 000°. A three-figure bearing uses three digits for clarity, so 37° is written as 037° when giving a bearing to the nearest degree. You must not measure counterclockwise simply because the smaller angle looks more natural. For a direction west of north, the clockwise bearing is close to 360°, not a small negative angle. Draw a curved arrow clockwise from the north reference as a visible reminder.
The four quadrants are a useful sanity check
A point north-east of an observer has a bearing between 000° and 090°. A point south-east has a bearing between 090° and 180°. A point south-west lies between 180° and 270°. A point north-west lies between 270° and 360°. This does not give the exact bearing, but it tells you when an answer is impossible. If the route clearly moves east and south, a result of 045° cannot be correct. Such a quadrant check often catches an incorrect inverse-tangent step. It is a quick way to protect the final answer before arithmetic errors become harder to trace.
Reverse bearings are directions in opposite senses
If the bearing of B from A is 060°, the bearing of A from B is 240°. You reverse the direction of a straight line by adding 180°, reducing by 360° if necessary. If the original bearing is 235°, the reverse is 055°. If it is 350°, the reverse is 170°. This arithmetic works when A and B are distinct points and the same north direction is used at both positions on the flat map model expected in the question. The crucial conceptual step is not memorising ‘+180’. It is recognising that the starting point and direction have both changed.
Why reverse direction is not ‘subtract from 360’
Students often calculate 360° minus the original bearing when they are asked for the reverse. That operation reflects a direction across the north–south axis rather than reversing the line. For instance, 360° − 060° = 300°, but the actual opposite of 060° is 240°. Sketch an arrow pointing north-east and reverse it: the new arrow must point south-west. The drawing makes the distinction clear. Whenever a formula seems easy, verify it against the quadrant. A calculation that gives the wrong quadrant cannot represent the requested reverse direction.
Every diagram should have parallel north lines
In ordinary planar bearing problems, the north reference lines at different points are parallel. That lets you use parallel-line angle relationships when a route contains two or more segments. At A draw a vertical arrow marked N. At B draw another parallel arrow marked N. When the first path AB has a stated bearing, transfer that information into a useful angle at the next point by examining the back bearing BA. Do not use a north arrow far away from the vertex as though every bearing were measured there. The parallel-line relationship is a tool; the point of observation remains decisive.
A right triangle turns east and north into a bearing
Suppose B lies 3 km east and 4 km north of A. The straight-line displacement has length √(3² + 4²) = 5 km. To determine the bearing of B from A, draw the angle clockwise from north. The angle is arctan(3/4), about 36.87°, giving a three-figure bearing of 037° to the nearest degree. The eastward distance is opposite the angle measured from north and the northward distance is adjacent. If you interchange them, you obtain 53.13°, which describes a different reference angle. Label the two legs and the angle before entering the ratio.
A south-east route needs its correct quadrant
Suppose a displacement is 6 km east and 8 km south. Its magnitude is 10 km. The angle east of south is arctan(6/8), approximately 36.87°. Because the clockwise bearing lies between east (090°) and south (180°), the bearing from north is 180° − 36.87° = 143.13°, or 143° to the nearest degree. You could obtain the same result by measuring 53.13° clockwise from east and adding 90°. Both approaches agree if the diagram is drawn correctly. The wrong answer 037° ignores the southward component and therefore fails the quadrant check.
North-west routes often need subtraction from 360
If B lies 5 km west and 12 km north of A, the displacement has magnitude 13 km. Its angle west of north is arctan(5/12), approximately 22.62°. Because the bearing is measured clockwise through almost a whole turn, the answer is 360° − 22.62° = 337.38°, or 337° to the nearest degree. Do not report 023° merely because that is the acute angle inside the triangle. The small angle describes an anticlockwise movement from north; the required bearing describes a clockwise movement. The three-figure notation signals which measurement you have chosen.
South-west routes need careful placement
If a point lies 8 km west and 6 km south of the observer, the displacement is 10 km. The angle west of south is arctan(8/6), about 53.13°. The clockwise bearing is 180° + 53.13° = 233.13°, or 233°. If a student writes 053°, the answer looks like a properly formatted three-figure bearing but points north-east instead. That is why typography is not a substitute for geometry. First confirm the region of the compass. Then calculate the angle within that region. Then express the final direction as a clockwise rotation from north.
A turn at B is not necessarily the bearing from B
Consider a route from A to B to C. The question may ask for the interior angle ABC, the change in travel direction at B, or the bearing of C from B. Those are distinct. To find angle ABC, use ray BA and ray BC, both starting at B. If AB has bearing 030°, then BA has bearing 210°. If BC has bearing 120°, the smaller angle between BA and BC is 90°. The interior angle at B is therefore a right angle. A careless student may compare AB’s 030° with BC’s 120° and get 90° by coincidence; with different values, that accidental method will fail.
Wrap-around angles require special care
Suppose AB has bearing 130°, so BA has bearing 310°. Suppose BC has bearing 040°. The directions at B straddle the 000° line. Their numerical difference is 270°, but the smaller angle between the rays is 360° − 270° = 90°. The interior angle ABC is therefore 90° if A, B and C form the intended non-degenerate triangle. This example shows why simply subtracting two bearings without sketching the rays can be wrong. For interior angles, consider the smaller included angle where the triangle lies, not automatically the raw numerical difference.
Sine and cosine rules extend bearings beyond right triangles
Not every navigation triangle has a right angle. If the question provides two sides and their included angle, the cosine rule may determine the third side. If a side and suitable opposite-angle pair are known, the sine rule may help find another angle. The bearing work comes before or after the triangle calculation: convert given directions into the correct interior angle, solve the geometry, and convert the final direction back into a three-figure bearing. Do not apply a right-triangle sine or tangent ratio to a non-right triangle. The K310 syllabus includes both the general triangle rules and bearing applications, so a well-labelled sketch is more important than memorising a single route formula.
Elevation and bearing are two separate angles
The previous Vol 0242 on three-dimensional trigonometry showed how a horizontal floor diagonal and vertical height form a right triangle for an angle of elevation. A bearing remains a horizontal direction, measured clockwise from north. An elevation angle tells you how high a line of sight rises above a horizontal reference. A single installation may require both, but they answer different questions. If the display is above the north-east corner, the bearing can be north-east even when its elevation angle is very steep. Do not report an elevation angle as the bearing simply because the two are computed from the same location.
Do not mistake a route length for a displacement
A visitor walks 3 km east and then 4 km north. They have walked 7 km along the two legs. Their straight-line displacement from the starting point is 5 km. The bearing of the endpoint concerns that resultant displacement, not the total path length. A question about distance travelled therefore may have a different answer from one about the straight-line distance between start and finish. Keep the words ‘journey’, ‘route’, ‘direct’ and ‘displacement’ distinct. This is the same care required when a real-world task includes detours, roads or an inaccessible area. The map’s story does not cancel the mathematics.
Accuracy, notation and an answer audit
The official K310 default accuracy instructions matter when the question does not specify otherwise. For non-exact numerical values, the syllabus gives three significant figures, or one decimal place for angles in degrees, unless the question sets a different accuracy; explicit accuracy questions need enough working to justify the result. When asked for a three-figure bearing, write it with three digits and obey any specified degree accuracy. A bearing of 037° is not ‘three significant figures’ in the usual numerical sense: its three-digit format communicates direction unambiguously. Keep extra accuracy during intermediate trig calculations. Include the degree symbol at the end and confirm that the direction is clockwise from the correct north line.
Find the first wrong step, not just the last answer
A wrong bearing may arise from the observer being reversed, the north line being drawn at the wrong point, the clockwise direction being ignored, a quadrant being mistaken, or a trigonometric ratio being inverted. A numerical slip is only one possible cause. Work backwards from the answer: Does the direction point into the correct quadrant? Was the angle measured from north? Are the triangle legs placed correctly? Does the length calculation make sense? A tutor can change just one condition and ask whether the learner’s method still holds. That test reveals whether the method is understood or merely remembered from an earlier diagram.
A calm bridge from primary maps to G3 geometry
Primary learners already read maps, identify directions, use simple scales and draw routes. The leap to G3 is the precision of angle measurement and the need to justify calculations across multiple linked triangles. Use the PSLE Learning Guide when scale, spatial interpretation or fractions remain unstable. Return to Vol 0238 on reading conditions for careful attention to constraints and Vol 0234 on line intersections for identifying the correct geometric relationships. The Mathematics route houses the broader subject skills. This article owns the specific bearings method rather than repeating a general geometry curriculum.
Thirty-one worked bearings checks: change the reference, then solve
Each invented practice case tests a distinct decision. Use a sketch for questions with a moving observer or a changed quadrant, then compare your method with the worked answer. The numbers do not come from a live examination paper. They are chosen to let you see the geometry clearly and recognise mistakes before speed becomes important.
1. Due east
Situation: A checkpoint is directly east of the starting point. Question: Give its bearing.
Working or model answer: 090°, because the clockwise turn from north to east is a right angle. Common trap: Do not write 90 without a leading zero when three-figure format is required. Check: Check the north arrow at the start. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
2. Due west
Situation: A station is directly west of the observer. Question: Give the bearing.
Working or model answer: 270°, measured clockwise from north. Common trap: Do not write 090° because east and west are opposite. Check: Confirm the arrow’s direction. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
3. Due south
Situation: The endpoint lies directly south. Question: State the bearing.
Working or model answer: 180°. Common trap: Do not confuse 180° with an angle of elevation. Check: The reference is horizontal north. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
4. North-east
Situation: An endpoint lies exactly halfway between north and east. Question: State the bearing.
Working or model answer: 045°. Common trap: Do not use 315°; that points north-west. Check: Quadrant before arithmetic. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
5. North-west
Situation: An endpoint lies 45° west of north. Question: Give the clockwise bearing.
Working or model answer: 315°, because 360° − 45° = 315°. Common trap: Do not report 045° for an anticlockwise turn. Check: Use a small clockwise arc. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
6. Reverse of 060°
Situation: The bearing of B from A is 060°. Question: Find the bearing of A from B.
Working or model answer: 060° + 180° = 240°. Common trap: Do not calculate 360° − 060° = 300°. Check: Reverse the arrow on the line. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
7. Reverse of 235°
Situation: A ray from A to B has bearing 235°. Question: Find B to A.
Working or model answer: 235° − 180° = 055°. Common trap: Do not retain 235°, which points the original way. Check: Use three digits for 055°. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
8. Reverse of 350°
Situation: B from A is 350°. Question: Find A from B.
Working or model answer: 350° − 180° = 170°. Common trap: Do not add 180° without reducing the rotation. Check: The reverse must point into the opposite quadrant. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
9. Reverse of 175°
Situation: The path from A to B is bearing 175°. Question: Find the reverse bearing.
Working or model answer: 175° + 180° = 355°. Common trap: Do not confuse near south with near north. Check: Check the directions differ by half a turn. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
10. 3 east, 4 north
Situation: B is 3 km east and 4 km north of A. Question: Find distance and bearing.
Working or model answer: The direct distance is 5 km; bearing arctan(3/4) ≈ 036.87°, hence 037° to the nearest degree. Common trap: Do not use arctan(4/3) for the angle from north. Check: Mark east as the opposite side. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
11. 4 east, 3 north
Situation: B is 4 km east and 3 km north. Question: Find its bearing.
Working or model answer: arctan(4/3) ≈ 53.13°, so 053° to the nearest degree. Common trap: Do not copy the previous 037° answer after swapping the legs. Check: The direction is more eastward than northward. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
12. 6 east, 8 south
Situation: A displacement moves east 6 km and south 8 km. Question: Give the bearing.
Working or model answer: 180° − arctan(6/8) ≈ 143°. Common trap: Do not place the route in the north-east quadrant. Check: The answer must lie between 090° and 180°. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
13. 8 west, 6 south
Situation: The endpoint is 8 km west and 6 km south. Question: Find the bearing.
Working or model answer: 180° + arctan(8/6) ≈ 233°. Common trap: Do not subtract the angle from 180°, which would point south-east. Check: Draw south first, then turn toward west. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
14. 5 west, 12 north
Situation: A point lies 5 km west and 12 km north. Question: Calculate its bearing.
Working or model answer: 360° − arctan(5/12) ≈ 337°. Common trap: Do not use a small positive bearing near north-east. Check: The route is north-west. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
15. 12 west, 5 south
Situation: A point lies 12 km west and 5 km south. Question: Calculate the bearing.
Working or model answer: 180° + arctan(12/5) ≈ 247°. Common trap: Do not accidentally report 293°, which points north-west. Check: The result must be between 180° and 270°. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
16. 12 north, 5 east
Situation: The endpoint is 12 m north and 5 m east. Question: Find the direct distance and bearing.
Working or model answer: The distance is 13 m; the bearing is arctan(5/12) ≈ 023° to the nearest degree. Common trap: Do not report 067°, the other acute angle. Check: The north component is larger, so the bearing is closer to 000°. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
17. 5 north, 12 west
Situation: The endpoint is 5 m north and 12 m west. Question: Find distance and bearing.
Working or model answer: The distance is 13 m; clockwise bearing is 360° − arctan(12/5) ≈ 293°. Common trap: Do not treat west of north as east of north. Check: Mark the correct quadrant. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
18. 6 north, 8 east
Situation: B is 6 km north and 8 km east of A. Question: Find distance and bearing.
Working or model answer: The displacement is 10 km, with bearing arctan(8/6) ≈ 053°. Common trap: Do not add 6 and 8 to obtain direct distance. Check: Pythagoras finds the hypotenuse. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
19. 800 north, 600 west
Situation: B lies 800 m north and 600 m west. Question: Find the direct distance and bearing.
Working or model answer: The displacement is 1000 m; bearing 360° − arctan(600/800) ≈ 323°. Common trap: Do not round the angle before deciding quadrant. Check: Keep units consistent. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
20. A route, not displacement
Situation: A walker travels 3 km east and 4 km north. Question: How far did the walker walk and how far from start?
Working or model answer: Distance travelled is 7 km; straight-line displacement magnitude is 5 km. Common trap: Do not apply Pythagoras to the path length. Check: Read the noun in the question. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
21. Angle at B
Situation: AB has bearing 030°. BC has bearing 120°. Question: Find angle ABC.
Working or model answer: BA has bearing 210°; between BA 210° and BC 120° the smaller included angle is 90°. Common trap: Do not compare AB and BC without reversing AB first. Check: Both rays defining angle ABC begin at B. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
22. Across north
Situation: AB has bearing 130°, while BC has bearing 040°. Question: Find the smaller angle ABC.
Working or model answer: BA has bearing 310° and BC 040°; their smaller angular separation is 360° − 270° = 90°. Common trap: Do not take the raw difference 270° as the interior angle. Check: The bearings straddle north. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
23. Another corner
Situation: AB is 315°, and BC is 045°. Question: Find angle ABC.
Working or model answer: BA is 135°; the included angle with BC 045° is 90°. Common trap: Do not use AB 315° as the direction from B. Check: Reverse first. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
24. An angle of elevation
Situation: The display rises 8 m above a point 15 m away horizontally. Question: Find the elevation angle.
Working or model answer: arctan(8/15) ≈ 28.1°. This is not a bearing because north direction is unspecified. Common trap: Do not label it 028° as though it were a compass direction. Check: Separate horizontal and vertical reference angles. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
25. Perspective drawing
Situation: A map picture looks as though the north line is tilted, but the compass rose defines up as north. Question: Which source controls?
Working or model answer: The stated orientation and geometrical data control, not the apparent lengths of the drawing. Common trap: Do not estimate a bearing by visual impression. Check: Redraw a clean plan. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
26. A right-angle claim
Situation: Two drawn lines look perpendicular but no right angle is marked or given. Question: May you apply right-triangle trigonometry?
Working or model answer: Not solely from appearance. Use supplied properties or derive the right angle first. Common trap: Do not invent a right angle to enable a familiar formula. Check: Identify the necessary evidence. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
27. A bearing around zero
Situation: A computed direction is 359.6° and the task requests the nearest degree. Question: How should it be described?
Working or model answer: The nearest whole-degree clockwise direction is 000° or equivalently 360°; follow the question’s convention, and recognise it is essentially north. Common trap: Do not write 360° as a distinct compass direction. Check: A full turn returns to north. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
28. A 090° reverse
Situation: A to B is due east at 090°. Question: Find B to A.
Working or model answer: 270°, due west. Common trap: Do not use 180°, which would be south. Check: Reverse the horizontal arrow. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
29. A changed endpoint
Situation: A triangle solution works, but the endpoint has moved to a different quadrant. Question: What must be recomputed?
Working or model answer: Retain any lengths still supported, but redraw the displacement and re-evaluate the bearing’s quadrant and reference angle. Common trap: Do not paste the previous bearing without checking the new geometry. Check: The method must survive changed conditions. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
30. A rounding step
Situation: The inverse tangent produces 36.8699° and the question requests a three-figure bearing to the nearest degree. Question: Write the result.
Working or model answer: 037°, with the leading zero and degree symbol. Common trap: Do not confuse three-figure notation with an instruction for three significant figures. Check: Apply the stated precision after the geometry is solved. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
31. An impossible bearing
Situation: A displacement is clearly south-west, but the answer shown is 064°. Question: Identify the fastest check.
Working or model answer: 064° lies north-east, contradicting both components; the result is wrong before considering the detailed calculation. Common trap: Do not trust a plausible decimal if its direction is impossible. Check: Use the quadrant as a final reasonableness test. The answer is reliable only if the north line, direction of travel and angle reference all match the wording.
Worked route: a complete exam response
A student begins at checkpoint A and walks 400 m east and then 300 m north to checkpoint B. Draw east horizontally right and north vertically up. The path travelled is 700 m, but the straight-line distance AB is √(400² + 300²) = 500 m. The bearing of B from A is measured clockwise from north at A. The northward adjacent side is 300 m and the eastward opposite side is 400 m. Therefore tan θ = 400/300, giving θ ≈ 53.13°. To the nearest degree, the bearing is 053°. The bearing of A from B is 233°. This complete answer identifies the direction, distinguishes path from displacement, and shows both the numerical and geometric checks.
Worked change: from a horizontal route to a height
Keep the same 400 m east and 300 m north plan, but suppose a hypothetical viewing point is vertically 120 m above checkpoint B. The horizontal straight-line run from A to the point directly beneath the viewing point is 500 m. The direct three-dimensional line of sight has length √(500² + 120²) = √264400 m, approximately 514 m to three significant figures. The angle of elevation is arctan(120/500) ≈ 13.5°. The horizontal bearing towards the point remains 053° because the vertical height does not change its horizontal direction. This is the crucial bridge to Vol 0242: bearing, elevation and distance can coexist without being interchangeable.
How to practise without memorising pictures
Choose a starting point on paper and write a displacement such as 8 units east and 6 units north. Solve the bearing and direct distance. Now switch north to south without changing the lengths. Next switch east to west. Finally reverse the observer. Four versions of the same numerical triangle should produce different compass bearings. Explain why after every version. Once this is comfortable, use a route with two segments and ask for the angle at their meeting point. A correct method should survive all those changes because it depends on reference directions, not on the shape of one familiar sketch.
A 20-minute diagnostic routine
Spend four minutes drawing north lines and identifying quadrants for eight directions. Spend four minutes reversing eight bearings and checking the directions by sketch. Use six minutes for two right-triangle displacement problems, keeping enough working to justify the ratios. Use four minutes to solve one included angle at a turning point and one problem distinguishing elevation from bearing. Reserve two minutes to inspect notation, units and the observing point. The suggested timing is a training plan, not an official per-topic allocation. Every mistake should be classified by its first wrong decision rather than simply counted as another lost mark.
How parents and tutors can help
Ask the learner: From which point are we looking? Where is north at that point? Which way do we turn? What quadrant should the answer occupy? These questions reduce guessing without supplying the answer. If the student has drawn the correct bearing but uses the wrong tangent ratio, the repair is trigonometry. If the student calculates correctly but measures from B instead of A, the repair is reading the question. A tutor can ask the learner to explain why the reverse bearing differs by 180° rather than just recite the rule. That explanation makes future unfamiliar diagrams much less threatening.
The independent-readiness test
A learner is ready when they can state four cardinal bearings, reverse any bearing, use perpendicular east-north or east-south components to calculate a distance and bearing, derive an interior angle between connected route segments, and distinguish a bearing from an elevation angle. They should check whether the stated route length differs from direct displacement and use sensible precision. If these tasks are stable, move to mixed trigonometry questions with more than one stage. If they fail, return to the earliest unstable step rather than rushing into a longer worksheet.
Related routes without duplicate intent
For the floor-diagonal and vertical-line-of-sight sequence, use Vol 0242. For combined English, Mathematics and Science constraints, use Vol 0244. The nearby Vol 0245 teaches compression of source information in English, a useful parallel to selecting the relevant data in a navigation question, but it is not a bearings substitute. The Mathematics route is the broader subject owner; the Secondary English Learning Hub and Science Hub remain subject routes rather than new owners of this specific geometry method. Keep this guide for bearings, north-line conventions, reversals and right-triangle route reasoning.
