Hello, Chez_!

A ship travelling with a constant speed and direction is signhted from a lighthouse.

At this time it's 2.7km away on a bearing of 42°.

Half an hour later, it is on a bearing of 115° at a distence of 7.6 km.

Find its speed in km per hour Code:

N A
: *
: 42° * \
: *2.7 \
: * \
L * 73° \ x
* \
* \
7.6* \
* \
* \
* B

Bearings are measured clockwise from North.

The lighthouse is at

The ship is first sighted when

The ship is sighted next when

. . and

We want the distance:

In , use the Law of Cosines:

. .

Hence: .

Now you can calculate its speed, right?