From North, clockwise, three digits: A three-figure bearing is the angle measured clockwise from North, written with three digits: due East is 090°, South is 180°, West is 270°. A small angle like 5° is written 005°.
Interactive: tap 060°, 135° or 290° to see the bearing measured clockwise from North as a three-figure angle.
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Always start at North: Draw a North arrow at the starting point, then sweep clockwise to the direction of travel.
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Compass directions as bearings: N = 000°, E = 090°, S = 180°, W = 270°. A bearing like N40°E means 40° clockwise from North = 040°; S30°W = 180° + 30° = 210°.
IB-style question — convert a direction
Express the direction 'South-East' as a three-figure bearing.
Step by step
- SE is halfway between S (180°) and E (090°), measured clockwise from N.
Final answer
135°.
Tap 135° — that's South-East, halfway between South (180°) and East (090°). Every bearing is read clockwise from North and written with three digits.
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Sketch the angle into a triangle: Most bearing problems become a triangle once you draw the North lines and mark the angles at each point.
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Reverse direction: add or subtract 180°: The back bearing (the bearing of A from B, given the bearing of B from A) is found by ±180°: add 180° if the bearing is under 180°, subtract 180° if it's 180° or more.
IB-style question — back bearing
The bearing of B from A is 070°. Find the bearing of A from B.
Step by step
- Under 180°, so add 180°.
Final answer
250°.
A bearing points one way (e.g. 070°); the BACK bearing points the exact opposite way — 180° round, so 070° + 180° = 250°. Picture the same arrow reversed.
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Keep it in 000°–360°: If adding 180° would exceed 360°, subtract instead — the back bearing always stays between 000° and 360°.
Journey problems become triangles: A two-leg journey on different bearings forms a triangle. Work out the interior angle at the turning point (from the two bearings and North lines), then use the cosine rule (two legs + included angle) for the direct distance.
IB-style question — distance home
A ship sails 8 km on a bearing of 060°, then 5 km on a bearing of 120°. Find its direct distance from the start.
Step by step
- Interior angle at the turn = 180° − (120° − 60°) = 120°.
- Cosine rule with the two legs.
Final answer
About 11.4 km.
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The journey as a triangle: 8 km from the start to the turn, then 5 km on to the end, with a 120° interior angle at the turn. The cosine rule on the two legs gives the direct distance d ≈ 11.4 km.
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Find the interior angle carefully: Use the North lines at the turning point to get the angle inside the triangle — it's rarely just the difference of the two bearings.