# 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 $A$ and $B$ be two points situated at two different places. 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 $B$. 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 $3$ digit number. So, for example, the bearing of west is $270^\circ$, and the bearing of northeast is $045^\circ$.

##### Example 1

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

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

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

## Changing directions

If the bearing of $B$ from $A$ is known, it is very easy to compute the bearing of $A$ from $B$; turning the opposite direction is the same thing as turning $180^\circ$, so the bearing of $A$ from $B$ must differ from the bearing of $B$ from $A$ by exactly $180^\circ$. In example $1$, the bearing of the ship from the dock is $60^\circ$, so the bearing of the dock from the ship must be $060^\circ + 180^\circ = 240^\circ$.

##### Example 2

*A child, (labelled $c$ in our diagram), throws their ball so that the bearing it travels at is $289^\circ$. The ball lands in a flowerbed (labelled $f$ in our diagram). What is the bearing of the child from the flowerbed?*

**

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

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

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

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