In surveying and air navigation, bearing are used to help identify the location of an object.
The four main directions of a compass are known as cardinal directions. They are north (N), east (E), south (S) and west (W).
A three-figure bearing are:
A $T$T is often but not always used to indicate a true bearing. If the angle measure is less than $100^\circ$100° it would be written something like 040° or 040°T.
To use true bearing to describe the location of a plane at point $B$B from the airport at point $A$A :
The true bearing of $B$B from $A$A is $127^\circ$127° or $127^\circ$127°$T$T.
The diagram below describes the bearing of $P$P from $O$O. Rotating clockwise from North, we get an angle of $55^\circ$55°.
Since this measure is less than three digits, we put a 0 in front of it so the true bearing of $P$P is 055°. Consider the true bearing of $O$O from $P$P . Since angle of elevation is equal to angle of depression and we are starting at $P$P the true bearing would be $180+55=235^\circ$180+55=235°.
A compass bearing describes the location of a point using:
To describe the position of point $B$B from $A$A we would say:
"Starting at South, I then rotate $53$53° towards East."
We can write this mathematically as:
Find the three-figure and the compass bearings of point $P$P from $O$O.
Starting at North rotate in a clockwise direction.
The three-figure bearing of $P$P from $O$O is $313^\circ$313°$T$T.
Point $P$P is closest to North, so starting at North, rotate $47^\circ$47° towards West.
The compass bearing of $P$P from $O$O is $N$N$47^\circ$47°$W$W.
The bearing needed or used completely depends on which position comes first. Have a look at the investigation below, it quickly shows you how the angle changes depending on if we are measuring the bearing of A from B or B from A.
Let's have a look at these worked examples.
Consider the point $A$A.
Find the true bearing of $A$A from $O$O.
What is the compass bearing of point $A$A from $O$O?
What is the true bearing of Southwest?
In the figure below, point $B$B is due East of point $A$A. We want to find the position of point $A$A relative to point $C$C.
Find the true bearing of point $A$A from point $C$C.
What is the compass bearing of point $A$A from point $C$C?