Bearings

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°.

Always start at North: Draw a North arrow at the starting point, then sweep clockwise to the direction of travel.

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°.

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.

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.

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.

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.