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Bearings

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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 AA​ and BB​ be two points situated at two different places. The bearing of BB​ from AA​ is calculated by measuring the angle clockwise from the north line through AA to the line from AA​ to BB. 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 33​ digit number. So, for example, the bearing of west is 270270^\circ, and the bearing of northeast is 045045^\circ​.


Example 1

A boat sets off from the dock at an angle 6060^\circ 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 6060^\circ. Bearings are always given in three figures, so you say that the bearing of the boat from the dock is 060060^\circ.


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



Changing directions

If the bearing of BB​ from AA​ is known, it is very easy to compute the bearing of AA​ from BB; turning the opposite direction is the same thing as turning 180180^\circ​, so the bearing of AA​ from BB​ must differ from the bearing of BB​ from AA​ by exactly 180180^\circ​. In example 11​, the bearing of the ship from the dock is 6060^\circ​, so the bearing of the dock from the ship must be 060+180=240060^\circ + 180^\circ = 240^\circ​.


Maths; Angles and geometry; KS4 Year 10; Bearings


​​Example 2

A child, (labelled cc in our diagram), throws their ball so that the bearing it travels at is 289289^\circ. The ball lands in a flowerbed (labelled ff 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 289289^\circ, as the ball landed in it and the bearing of the ball's flight was 289289^\circ.


The bearing of the child from the flowerbed must differ from the bearing of the flowerbed from the child by 180180^\circ, and it must be given in degrees as a three-digit number between 000000^\circ and 360360^\circ.


289+180>360289^\circ + 180^\circ > 360^\circ​, so the only possible value for the bearing of the child from the flowerbed must be 289180=109289^\circ - 180^\circ = 109^\circ.


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


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