Linear motion with bearings

Example

A crow leaves its base to deliver a message to a castle which is located 125 km away on a bearing of 075°.

It then flies 100 km to another castle on a bearing of 220°.

What is the displacement of the crow from its base?

What bearing must the crow fly to return to base ?

 

Solution

Refresher for Trigonometry with bearings

 

 

Using the cosine rule

The crow is displaced 71.7 km (1dp)

 

To find the bearing of the crow from its base, the angle between the two castles and the base can be calculated :

 

or