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HSC · Topic explainer

True bearings in HSC Mathematics Standard 2

A true bearing is an angle measured clockwise from true north at the starting point. Write it with three digits, such as 060° for a direction 60° east of north. North is 000° and east is 090°. To find a back bearing, reverse the direction by 180° and express the result from 000° up to, but below, 360°.

Worked example

A boat travels from A to B on a true bearing of 060°. Draw a north line through A, then measure 60° clockwise from that line to the direction of travel.

For the return direction, draw a new north line through B. The ray from B to A points 180° away from the outgoing direction, so 060° + 180° gives a return bearing of 240°. When the outgoing bearing is 180° or more, subtract 180° instead.

Parallel north lines through A and B. The segment from A up and right to B is at 060 degrees clockwise from north. The reverse direction from B to A is at 240 degrees clockwise from north.

Official exam practice

Find other years and marking guidance in the Mathematics Standard 2 official exam archive.