1. ## bearing

Im not sure how to draw this and so i havnt been able to try and solve it yet, so if you could help me draw it and give a few hits that would be great thnx

A ship travelling with a constant speed and direction is signhted from a lighthouse.At this time it's 2.7kn away on a bearing of 42degrees. half an hour later it is ona bearing of 115degrees at a distence of 7.6 km from the same lighyhouse. find its speed in km per hour

thank you

2. 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 $\displaystyle L.$

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

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

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

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

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

Now you can calculate its speed, right?