Bearings and scale drawings Worked Solutions — GCSE Maths

Count the figures in the angle that is given.

$72$ has $2$ figures, and a bearing needs three, so zeros must be put in at the front.

Put in the zeros needed at the front.

Writing $1$ zero in front of $72$ gives $072$. The zeros do not change the size of the angle at all.

State the three-figure bearing.

The direction is the bearing $072^\circ$.

Count the figures in the angle that is given.

$8$ has $1$ figure, and a bearing needs three, so zeros must be put in at the front.

Put in the zeros needed at the front.

Writing $2$ zeros in front of $8$ gives $008$. The zeros do not change the size of the angle at all.

State the three-figure bearing.

The direction is the bearing $008^\circ$.

Work out the angle turned clockwise from north.

The eight compass points are $45^\circ$ apart, so starting at north and turning clockwise to north-east is a turn of $45^\circ$.

Write the angle with three figures.

$45^\circ$ is written as $045^\circ$, because a bearing always uses three figures.

State the three-figure bearing.

The direction north-east is the bearing $045^\circ$.

Work out the angle turned clockwise from north.

The eight compass points are $45^\circ$ apart, so starting at north and turning clockwise to south-west is a turn of $225^\circ$.

Write the angle with three figures.

$225^\circ$ is written as $225^\circ$, because a bearing always uses three figures.

State the three-figure bearing.

The direction south-west is the bearing $225^\circ$.

Write down the bearing that is given, and note that the north lines at A and B are parallel.

Standing at $A$ and facing north, you turn $070^\circ$ clockwise to look at $B$. North points the same way at $B$, so the two north lines are parallel and the two bearings must differ by $180^\circ$.

Add or subtract $180$ degrees to reverse the bearing.

$070^\circ$ is less than $180^\circ$, so add $180^\circ$: $070 + 180 = 250$.

State the bearing of A from B.

The bearing of $A$ from $B$ is $250^\circ$.