# bearing

• Mar 19th 2008, 02:17 PM
Chez_
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
• Mar 19th 2008, 03:18 PM
Soroban
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?