lesson
Measure clockwise from north
1 · Learn
A bearing is an angle measured clockwise from north, written with three digits. Due east is 090°, south 180° and west 270°. Draw a north line at the point from which the bearing is measured.
A reverse bearing differs by 180°, adjusted into the interval from 000° up to 360°. Do not confuse a bearing from A to B with one from B to A.
2 · Worked example
If B is on a bearing of 065° from A, A is on a bearing of 245° from B, assuming parallel north lines in the diagram.
3 · Your turn
Find the reverse bearing of 310°.
Check your answer
130°.
4 · Apply your learning
Draw the two north lines and use angle facts to justify the reverse direction.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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