A scale (e.g. "$1\text{ cm represents } 200\text{ m}$") lets you shrink real-world distances onto paper proportionally. To find a real distance, measure it on the drawing with a ruler, then multiply by the scale. To find a length to draw, divide the real distance by the scale.

A ratio scale means "$1$ unit on the drawing represents $50\,000$ of the same unit in real life" — so if the drawing is in centimetres, $1\text{ cm}$ represents $50\,000\text{ cm}$, which you then convert into a more sensible unit (here, $500\text{ m}$, since $50\,000 \div 100 = 500$). Always convert the real-world answer into metres or kilometres at the end rather than leaving it in an awkward number of centimetres.

A bearing gives a direction as an angle measured clockwise from north, always written using three digits (e.g. $025°$, not $25°$). Bearings run from $000°$ to $360°$, so north itself is $000°$ (or equivalently $360°$), east is $090°$, south is $180°$, and west is $270°$.

Draw a quick sketch with north lines at both points. Because the north lines at $A$ and $B$ are parallel, alternate angles let you connect the two bearings:

• If the given bearing is less than $180°$, add $180°$.
• If the given bearing is $180°$ or more, subtract $180°$.

A typical question gives a bearing and a distance from a starting point (e.g. "a ship sails $8\text{ km}$ on a bearing of $070°$"). Draw a north line at the start point, use a protractor to mark the bearing angle clockwise from it, then use your scale to mark off the correct length along that direction.

The bearing of $B$ from $A$ is $025°$. Find the bearing of $A$ from $B$.

1. Since $025°$ is less than $180°$, add $180°$: $025° + 180° = 205°$.
2. The bearing of $A$ from $B$ is $205°$.

A map has a scale of $1 : 25\,000$. Two towns are $6.4\text{ cm}$ apart on the map. Find the real distance between them in kilometres.

1. Real distance $= 6.4 \times 25\,000 = 160\,000\text{ cm}$.
2. Convert cm to m ($\div 100$): $160\,000 \div 100 = 1600\text{ m}$.
3. Convert m to km ($\div 1000$): $1600 \div 1000 = 1.6\text{ km}$.