8.06 Extension: Bearings

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).

Three-figure (true) bearings

A three-figure bearing are:

• measured from north ($N$N)
• measured in a clockwise direction
• written using three figures

 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 :

1. place the center of a compass on the starting point, in the case the airport.
2. starting at North, rotate clockwise until we get to the line $AB$AB. 
3. write angle as the true bearing of point $B$B.

 

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°.

 

Compass bearings

A compass bearing describes the location of a point using:

• the starting direction of either north or south;
• the acute angle needed to rotate
• the direction to rotate, east or west.

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:

$S$S$53$53°$E$E

 

Worked example

Question 1

Find the three-figure and the compass bearings of point $P$P from $O$O.

Think: To find the three-figure bearing, we want to find the measure of the angle that has initial side on the North axis, and terminal side on $PO$PO.

Do: Subtract the angle from $360^\circ$360°. We have $360^\circ-47^\circ=313^\circ$360°−47°=313° 

Therefore, the three-figure bearing of $P$P from $O$O is $313^\circ$313°$T$T.

Think: Point $P$P is closest to North

Do: 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.

 

Exploration

The bearing needed or used completely depends on which position comes first.  Have a look at the applet below. It quickly shows you how the angle changes depending on if we are measuring the bearing of $A$A from $B$B or $B$B from $A$A.

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Practice questions

Question 2

Question 3

Question 4