IB Maths AA 3.3 Notes

Bearings

Applied trigonometry uses the ideas from right-angled and non-right-angled triangles to solve real problems. These problems often involve distances, heights, angles, bearings, and constructing a diagram from a written description. In this section, labelled diagrams are especially important because they help identify which trigonometric method to use.

A bearing gives the direction from a point A to a point B. Bearings are measured:

• from north
• clockwise
• using three figures

So east is written as $090^\circ$, south as $180^\circ$, and west as $270^\circ$.

Image description: compass diagram showing north, east, south and west, with a bearing measured clockwise from north.

Finding a bearing is simple, but problems will often ask you to calculate a reverse bearing. A reverse bearing is a bearing taken from point B to point A. This is simply calculated as:

$\textrm{Reverse bearing = bearing } + 180^\circ$

If this goes over 360°, then subtract 360° to bring the bearing back into the first revolution. Let's practice this:

The bearing of $B$ from $A$ is $058^\circ$. Find the bearing of $A$ from $B$.

The reverse bearing differs by $180^\circ$.

$058^\circ+180^\circ=238^\circ$.

So the bearing of $A$ from $B$ is $238^\circ$.

If adding $180^\circ$ gives a number greater than $360^\circ$, subtract $360^\circ$.

The bearing of $Q$ from $P$ is $315^\circ$. Find the bearing of $P$ from $Q$.

$315^\circ+180^\circ=495^\circ$.

$495^\circ-360^\circ=135^\circ$.

So the bearing of $P$ from $Q$ is $135^\circ$.