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Explainer Video

Tutor: Dylan

Summary

Bearings

​​In a nutshell

You can use bearings to describe the direction of one place or object in relation to another. In this lesson, you will learn how to read and measure the bearing of one place or object from another.



What are bearings?

Let AAA​ and BBB​ be two points situated at two different places. The bearing of BBB​ from AAA​ is calculated by measuring the angle clockwise from the north line through AAA to the line from AAA​ to BBB. More generally, the bearing of a specific direction is given by measuring the angle clockwise from the north line to that direction. Bearings are always given in degrees, and as a 333​ digit number. So, for example, the bearing of west is 270∘270^\circ270∘, and the bearing of northeast is 045∘045^\circ045∘​.


Example 1

A boat sets off from the dock at an angle 60∘60^\circ60∘ clockwise from north. What is the bearing of the boat from the dock?


Maths; Angles and geometry; KS4 Year 10; Bearings


The angle swept out from the north line through the dock to the line from the dock to the boat is 60∘60^\circ60∘. Bearings are always given in three figures, so you say that the bearing of the boat from the dock is 060∘060^\circ060∘.


Therefore, the bearing of the boat from the dock is 060∘‾\underline{060^\circ}060∘​.



Changing directions

If the bearing of BBB​ from AAA​ is known, it is very easy to compute the bearing of AAA​ from BBB; turning the opposite direction is the same thing as turning 180∘180^\circ180∘​, so the bearing of AAA​ from BBB​ must differ from the bearing of BBB​ from AAA​ by exactly 180∘180^\circ180∘​. In example 111​, the bearing of the ship from the dock is 60∘60^\circ60∘​, so the bearing of the dock from the ship must be 060∘+180∘=240∘060^\circ + 180^\circ = 240^\circ060∘+180∘=240∘​.


Maths; Angles and geometry; KS4 Year 10; Bearings


​​Example 2

A child, (labelled ccc in our diagram), throws their ball so that the bearing it travels at is 289∘289^\circ289∘. The ball lands in a flowerbed (labelled fff in our diagram). What is the bearing of the child from the flowerbed?

Maths; Angles and geometry; KS4 Year 10; Bearings

​


The bearing of the flowerbed from the child must be 289∘289^\circ289∘, as the ball landed in it and the bearing of the ball's flight was 289∘289^\circ289∘.


The bearing of the child from the flowerbed must differ from the bearing of the flowerbed from the child by 180∘180^\circ180∘, and it must be given in degrees as a three-digit number between 000∘000^\circ000∘ and 360∘360^\circ360∘.


289∘+180∘>360∘289^\circ + 180^\circ > 360^\circ289∘+180∘>360∘​, so the only possible value for the bearing of the child from the flowerbed must be 289∘−180∘=109∘289^\circ - 180^\circ = 109^\circ289∘−180∘=109∘.


Therefore, the bearing of the child from the flowerbed is 109∘‾\underline{109^\circ}109∘​.


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FAQs - Frequently Asked Questions

Which way do bearings go in maths?

The bearing of B from A is calculated by measuring the angle clockwise from the north line through A to the line from A to B.

What are bearings used for?

You can use bearings to describe the direction of one place or object in relation to another.

How do I calculate bearings?

The bearing of a specific direction is given by measuring the angle clockwise from the north line to that direction.

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