a ship travelling with a constant speed and direction is sighted from a lighthouse.
at this time it is bearing of 042.
half an hour later on a bearing of 115 at a distance of 7.6km from the same lighthouse.
find its speed in km per hour

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- anonymous

MissMysterioulsyStupid, have you given us all the information? Are you possibly missing another distance?

- anonymous

oh sorry i missed out 2.7
its a ship travelling with a constant speed and direction is sighted from a lighthouse.
at this time it is 2.7 km bearing of 042.
half an hour later on a bearing of 115 at a distance of 7.6km from the same lighthouse.
find its speed in km per hour

- anonymous

Okay - now I can help you.

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## More answers

- anonymous

thx

- anonymous

You just have to use the cosine rule. Have you got a picture of what the setup is supposed to look like?

- anonymous

no, were supposed to work it out ouselves
and i dunno how to do bearings

- anonymous

Bearings always start from due north (0 degrees) , and when you trace out an angle (e.g. 42 degrees) you do so in a clockwise direction.

- anonymous

So, draw a small vertical line to represent your lighthouse, then put your pen flat on the page along the lighthouse and turn it about 42 degrees. Put a point somewhere after you've turned and draw a line from that point to your lighthouse.

- anonymous

Next, all you have to do is repeat the whole angle sweeping thing with your pen again, this time for the new angle. So starting from due north, sweep about 115 degrees clockwise and mark another point. Now just draw a line from the lighthouse to that point.

- anonymous

Finally, draw a line between your two points - this will be the path the ship has taken. Oh, I forgot to tell you to make the 115 degree line with 7.6km.

- anonymous

ok, ive got a traingle
i think its right

- anonymous

Okay, nearly there...the angle closest to the lighthouse is going to be 115 degrees - 42 degrees (because we just want the angle that's living in the triangle). That should work out to 73 degrees.
If you label the unknown distance (the distance between your points, which is the distance the ship has traveled) with something like, 'd', you have everything that's needed for the cosine rule (you can use the cosine rule in any plane triangle when you have two sides and the angle IN BETWEEN given)).

- anonymous

I won't leave you hanging - I'll do the mathematics, but I hope everything was explained well enough for you to be able to do it yourself...
\[d^2=(2.7)^2+(7.6)^2-2(2.7)(7.6)\cos(73)\approx53.05km^2\]

- anonymous

Taking the square root of both sides gives you the distance traveled:\[d \approx 7.28km\]which sounds reasonable.
The speed is just the amount of distance it covers per unit time, so\[speed=\frac{7.28km}{0.5h}=14.57km/h\]

- anonymous

i got the d as 7.1 :S
dont u do the pythagorus theorum there?

- anonymous

No, Pythagoras' Theorem is only applicable to right-angled triangles. That's the trick - they want you to use either the sine or cosine rule to get your answer.

- anonymous

oh ok thx

- anonymous

No probs.

- anonymous

ur a life saver:)
*bow* *bow*

- anonymous

Why, thank you :p

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