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# Sine and Cosine Rule - Bearings Watch

1. Can I get some help on this question.

A ferry and a cargo ship are both approaching the same port. The ferry is 3.2 km from the port on a bearing of 076° and the cargo ship is 6.9 km from the port on a bearing of 323°.

Find the distance between the two vessels and the bearing of the cargo ship from the ferry.

Here is a diagram which I draw from extracting the info from the question to help me answer this

Is it any correct because it's not helping me, I don't know where to start.

2. The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
3. I don't understand, how is that.
4. pretty sure you do this:

angle at cargo is 37 degrees, use the sine rule to get angle at ferry and then use the fact that angle in a triangle add up to 180 and once you got that, use the cosine rule to to get x
5. (Original post by generalebriety)
The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
Really?

(Original post by uer23)
I don't understand, how is that.
The angle between the line of 0 degrees and the horizontal line is 90 degrees, you know the bearing is 76 degrees, so 90-76 = 14.
6. This should be your diagram:
Attached Images

7. (Original post by assmaster)
Really?

The angle between the line of 0 degrees and the horizontal line is 90 degrees, you know the bearing is 76 degrees, so 90-76 = 14.
Oh so that means you need a bearing from North to go 76 degrees.
8. (Original post by boromir9111)
angle at cargo is 37 degrees
I don't understand how this was deduced ( I can't spot and interior/exterior, alternate or any other type of angles).
9. (Original post by generalebriety)
The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
is it because 76 + 24 = 90?
10. (Original post by uer23)
I don't understand how this was deduced ( I can't spot and interior/exterior, alternate or any other type of angles).
360-323=37
11. Thanks a lot for your help guys I have worked it out finally.
12. (Original post by assmaster)
Really?
(Original post by zdo0o)
is it because 76 + 24 = 90?
What are you, my primary school? I don't know my times tables either! And I'm proud of it!

(Yes, 14. Thank you. )
13. Just need to make sure this is correct as I don't have the answer to this question, can someone check to see if it is right.

1) Using cosine rule to find Side

2) Using sin rule to find angle

=

=

=

=

=

3) Bearing of cargo ship from ferry

Bearing of cargo ship from ferry =

14. (Original post by generalebriety)
What are you, my primary school? I don't know my times tables either! And I'm proud of it!

(Yes, 14. Thank you. )
incidentally, i do actually teach year 6 maths at a primary school as part of my gap-year-ing, and i don't know my times tables either
15. Oh you drew the picture wrong, that makes sense now but yeah your method seems right.
16. (Original post by boromir9111)
Oh you drew the picture wrong, that makes sense now but yeah your method seems right.
Oh really ? Would you please show me how you would draw the picture.
17. dude look at your first drawing and compare it to the second, quite a big change there and changes how you solve for it (makes it easier now) but that's what i meant, your first drawing was wrong, pay attention and not lash out on me.
18. (Original post by boromir9111)
dude look at your first drawing and compare it to the second, quite a big change there and changes how you solve for it (makes it easier now) but that's what i meant, your first drawing was wrong, pay attention and not lash out on me.
huh? I was not lashing out on you. I thought your comment was referring to my post with the solutions, where you said 'you drew the picture wrong'. So I thought maybe you can show me how it is supposed to be drawn. Be a bit more clear next time.

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