Geometry

Bearings

Measure a direction clockwise from north.

Predict, test and explain

Step 1 of 3

Predict

An outward bearing is 060°. What is the return bearing?

bearing A→B=060∘\text{bearing }A\to B=060^\circ
NN
EE
SS
WW
AA
BB

Scroll the diagram sideways to see every label.

AB=4 kmAB=4\,\text{km}

Bearings use three digits and are measured clockwise from north. A full turn has the same direction as 000°.

InvestigateWhy is east a bearing of 090 degrees?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

The bearing of B from A is 075 degrees. Find the bearing of A from B, assuming parallel north lines.

Hint

Reverse the direction by half a turn and write the result as three digits.

Reveal answer

The return bearing is 255 degrees.

075∘+180∘=255∘075^\circ+180^\circ=255^\circ

Build an explanation

Hint 1

Start from north at the point where the journey begins.

Hint 2

Measure clockwise and write the bearing with three digits.

Hint 3

The return bearing differs by 180°; add or subtract 180° to keep it below 360°.

Worked example

This example uses fixed values, separate from the diagram controls.

The bearing from A to B is 060°. Find the bearing from B to A.

  1. Use north at B for the return journey.
  2. Add 180° to 060°: 60° + 180° = 240°.

Answer: 240°.

Connect this idea

Watch out: Bearings are measured clockwise from north, rather than from the previous line of travel.