We can use trigonometry to answer some bearings questions, provided that we have sufficient information.

It is always useful to draw a quick sketch of the situation from the information given in the question. The diagram does not have to be at all accurate.

**Example**

A boat is due South of a lighthouse and sails on a bearing of 292º for 51 km until it is due West of the lighthouse. How far away is it now from the lighthouse (to 3 sig. figs.)?

**Answer**

Draw a sketch using the information given and work out the relevant angles in the right-angled triangle.

Here the interior angle = 360 - 292 = 68º

We want to find the side length LW.

Set up the trig equation to get:

sin68º = LW/51

LW= 51 sin68º

LW = 51 x 0.92718....

LW= 47.3** **(3 s.f.)

Answer is **47.3 km**