lesson
Represent a three-dimensional arrangement accurately
1 · Learn
A plan is the view from above. Front and side elevations are orthogonal views, so visible width and height must come from the stated direction rather than perspective. Hidden depth can disappear in an elevation.
A bearing is measured clockwise from north and written with three digits, such as 065°. Draw a north line at the starting point before measuring. The reverse bearing differs by 180°, adjusted to stay between 000° and 360°.
Scale and labels matter. Do not measure a not-to-scale screen diagram when dimensions are supplied.
2 · Worked example
A cuboid 8 cm wide, 5 cm deep and 3 cm high has an 8×5 plan, an 8×3 front elevation and a 5×3 side elevation. The reverse of bearing 070° is 250°.
3 · Your turn
State the three rectangular views of a 6 by 4 by 2 cuboid. Find the reverse bearing of 135°.
Check your answer
Plan 6×4, front 6×2, side 4×2; reverse bearing 315°.
4 · Apply your learning
Build or sketch a labelled block model, then draw its three orthogonal views on the grid pad with a north-arrow bearing example.
Adult guidance and safety
This is England national-curriculum core teaching, not an exam-board specification. Check prerequisite understanding, require clear working and use additional varied practice before judging fluency.
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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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