What bearing is due east? due south? due west?

090^\circ, 180^\circ, 270^\circ

What bearing is due north?

000^\circ (three figures; 360^\circ is not used)

How do you find a back bearing?

Add 180^\circ if the bearing is less than 180^\circ; subtract 180^\circ if it is 180^\circ or more.

What does a scale of 1:50\,000 mean?

1 cm on the map is 50\,000 cm (0.5 km) in real life.

How do you change a map distance to a real distance?

Multiply by the scale number, then convert the units.

How do you change a real distance to a map distance?

Change to the same units, then divide by the scale number.

A map has scale 1:25\,000 and two towns are 8 cm apart. Real distance?

8\times25\,000=200\,000 cm =2 km

Why do bearing problems often involve right-angled triangles?

North, east, south and west lines are at 90^\circ to each other.

Which tools do you use to solve bearing problems?

Pythagoras, SOH CAH TOA and back bearings, with a sketch and north lines.

What should a scale drawing include?

A scale, a north line at each turn, bearings measured clockwise, and distances drawn to scale.

Bearings and scale drawingIB MYP Maths Extended: Flashcards

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How is a bearing measured?

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How is a bearing measured?: Clockwise from north, using three figures.
Write $45^\circ$ as a bearing.: $045^\circ$
What bearing is due east? due south? due west?: $090^\circ$ , $180^\circ$ , $270^\circ$
What bearing is due north?: $000^\circ$ (three figures; $360^\circ$ is not used)
How do you find a back bearing?: Add $180^\circ$ if the bearing is less than $180^\circ$ ; subtract $180^\circ$ if it is $180^\circ$ or more.
Bearing of $B$ from $A$ is $130^\circ$ . Bearing of $A$ from $B$ ?: $130^\circ+180^\circ=310^\circ$
Bearing of $B$ from $A$ is $250^\circ$ . Bearing of $A$ from $B$ ?: $250^\circ-180^\circ=070^\circ$
What does a scale of $1:50\,000$ mean?: $1$ cm on the map is $50\,000$ cm ( $0.5$ km) in real life.
How do you change a map distance to a real distance?: Multiply by the scale number, then convert the units.
How do you change a real distance to a map distance?: Change to the same units, then divide by the scale number.
A map has scale $1:25\,000$ and two towns are $8$ cm apart. Real distance?: $8\times25\,000=200\,000$ cm $=2$ km
Why do bearing problems often involve right-angled triangles?: North, east, south and west lines are at $90^\circ$ to each other.
Which tools do you use to solve bearing problems?: Pythagoras, SOH CAH TOA and back bearings, with a sketch and north lines.
What should a scale drawing include?: A scale, a north line at each turn, bearings measured clockwise, and distances drawn to scale.

Exam questions on Bearings and scale drawing

A ship sails from port $A$ to port $B$ on a bearing of $072^\circ$ . Port $C$ is on a bearing of $162^\circ$ from $B$ .
Find the size of angle $ABC$ .2 marks
A map of an island has a scale of $1:50\,000$ . The villages Karu and Mele are $6.4$ cm apart on the map.
Another map of the island has a scale of $1:25\,000$ . Find the distance between Karu and Mele on this map.2 marks
A walker leaves a hut $H$ and walks $8$ km on a bearing of $040^\circ$ to a lake $L$ . She then walks $6$ km on a bearing of $130^\circ$ to a summit $S$ .
Show that angle $HLS$ is $90^\circ$ and hence find the straight-line distance $HS$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).