Directions and Bearings (Ex 6D)

Year 10 Mathematics Core · Cambridge Ch 6, §6D · Mr Wong

Name

Class

Date

Learning intentions.

Read and write true bearings (clockwise from north, 3 digits, °T)
State the reverse bearing of a given direction (±180°)
Combine bearings with right-triangle trig to find east/north distances

Key results — true bearings

Measured clockwise from due north · written as 3 digits + °T · range 000°–360° · reverse differs by 180°

$N=000°T,\;NE=045°T,\;E=090°T,\;SE=135°T,\;S=180°T,\;SW=225°T,\;W=270°T,\;NW=315°T$

Warm-up

1. Write each cardinal direction as a true bearing.

a N =

b NE =

c E =

d SE =

e S =

f SW =

g W =

h NW =

2. State the reverse (opposite) bearing.

a $020°$T →

b $262°$T →

c $155°$T →

d $344°$T →

3. $A$, $B$, $C$, $D$ lie around origin $O$ as shown. Give the true bearing of each from $O$.

a $A=$

b $B=$

c $C=$

d $D=$

Part A — Stating a direction

4. Using the diagram in Q3, state the true bearing of $O$ from each point.

a $O$ from $A=$

b $O$ from $B=$

c $O$ from $C=$

d $O$ from $D=$

Trig 6D — continued

Part B — Bearings with trigonometry

Name

Part B — Bearings with trigonometry

Draw a labelled diagram with a north arrow at the start. Then form a right triangle and solve to 2 d.p.

5. A ship sails due south for $5$ km and then on a bearing of $120°$T for $11$ km. (a) How far east of the start? (b) How far south of the start?

6. A plane flies $100$ km on a bearing of $070°$T. (a) How far east of the start? (b) How far north of the start?

7. A hiker walks $6$ km on a bearing of $215°$T. (a) How far west of the start? (b) How far south of the start?

8. A boat sails due north for $4$ km, then on a bearing of $050°$T for $5$ km. (a) How far east of the start? (b) What is its total distance north of the start?

9. Challenge. A drone flies on bearing $110°$T for $4$ km, then changes to bearing $200°$T for $3$ km. Find the bearing of the drone's final position from its start (1 d.p.). Hint: find the east and north displacements after each leg, sum them, then use trig.