17.5 Bearings and scale drawings — Learn

Prerequisites: use a protractor, measure a line segment and multiply or divide with decimals.

Objectives: measure lengths and angles, interpret and draw scale plans, use compass directions, and write three-figure bearings. This page covers G15.

Bearings

A bearing gives a direction as an angle measured clockwise from north. Write it with three digits, adding zeros at the front when needed. For example, east is $090^\circ$ and south-west is $225^\circ$.

Worked example. A path goes from the south-west corner of a rectangle to its north-east corner. Find its bearing from the start if the rectangle is $24$ m east-west and $18$ m north-south.

• The path's eastward component is $24$ m and its northward component is $18$ m.
• The angle east of north is $ an^{-1}(24/18)$, about $53.1^\circ$.
• A bearing turns clockwise from north, so the bearing is about $053^\circ$.

For a hand-drawn direction, place the protractor centre at the start and align zero with north. Measure clockwise.

Scale drawings

A scale compares a drawing length with a real length. At scale $1$ cm represents $3$ m, divide real lengths by $3$ to find centimetres on the plan.

Worked example. Draw the $24$ m by $18$ m garden at $1$ cm to $3$ m.

• $24 \div 3 = 8$, so draw the east-west side as $8$ cm.
• $18 \div 3 = 6$, so draw the north-south side as $6$ cm.
• Measure the diagonal: $\sqrt{8^2+6^2}=10$ cm, representing $30$ m.

Watch out. A bearing is not measured from the nearest compass direction. Start at north and turn clockwise; write three digits, such as $053^\circ$.

Progress check

The plan is drawn at $1$ cm for $3$ m, and its diagonal measures $10$ cm. Work out the real path length. Compare it with your first estimate, and explain what the bearing $053^\circ$ tells you.

You should now be able to

• measure line segments and angles accurately;
• use compass points and three-figure bearings;
• convert between lengths on a scale drawing and real lengths;
• check a direction angle from north, clockwise.