bearing

Hello, Chez_!

Quote:

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 $L.$

The ship is first sighted when $\angle NLA = 42^o,\;LA = 2.7\text{ km}$

The ship is sighted next when $\angle NLB = 115^o\quad\Rightarrow\quad \angle ALB = 73^o$
. . and $LB = 7.6\text{ km}$

We want the distance: $x \:=\:AB$

In $\Delta ALB$ , use the Law of Cosines:
. . $x^2 \;=\;2.7^2 + 7.6^2 - 2(2.7)(7.6)\cos73^o \;=\;53.05106524$

Hence: . $x \;=\;7.28361622\text{ km}$

Now you can calculate its speed, right?