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1. bearings question
An aeroplane flies from airport A to airport B 80 km away on a bearing of 070∘. From B the aeroplane flies to airport C, 60 km from B. Airport C is 90 km from A. Find the two possible directions for the course set by the aeroplane on the second stage of its journey.
I got theta to be 78.6 but I can't work out the bearings, for some reason I keep getting the wrong answer when trying to figure it out as shown below:

I do 360 - (70 + 2(78.6)) and get 132.8 which is incorrect and this is for only one of the bearings, I have no idea how to work out the other, I just keep seeing it as from due north, but the answer is 323.6...

thanks

2. Re: bearings question
I do not see how theta is 78.6

The Cosine Rule gives a different answer

the 70 marked in your diagram is not correct ... why do you think that C1 is North of B
3. Re: bearings question
(Original post by TenOfThem)
I do not see how theta is 78.6

The Cosine Rule gives a different answer

the 70 marked in your diagram is not correct ... why do you think that C1 is North of B
I done: costheta = (6^2+8^2-9^2)/(2*6*8) then found theta to be 78.6

Does it really matter where C1 is, as it's just asking for the two possible directions
4. Re: bearings question
Sorry, yes the 78.6 is right (I used 70 instead of 60 because of your diagram )
5. Re: bearings question
(Original post by zoxe)
Does it really matter where C1 is, as it's just asking for the two possible directions
The 2 possible positions of C are defined by the angle theta
6. Re: bearings question
(Original post by zoxe)
...
Whilst I agree with 78.6, I can't see why you're doing "360 - (70 + 2(78.6))", and I don't agree with the book; I make it 328.6 for one.
7. Re: bearings question
(Original post by ghostwalker)
Whilst I agree with 78.6, I can't see why you're doing "360 - (70 + 2(78.6))", and I don't agree with the book; I make it 328.6 for one.
How did you get 328.6? I'm doing 360-(70+2(78.6)) because all the angles add up to 360 around the point B, two of those angles are theta, i.e 78.6 and the other is 70. The book has done 180 + 70 - theta and 180 + 70 - theta and I can see what theyve done and how they have done it but I don't really know why the way i'm doing it does not work.
8. Re: bearings question
(Original post by ghostwalker)
Whilst I agree with 78.6, I can't see why you're doing "360 - (70 + 2(78.6))", and I don't agree with the book; I make it 328.6 for one.
also, you are right, the book is wrong on one of them.
9. Re: bearings question
i get
328.6 and 171.4
Last edited by TenOfThem; 09-07-2012 at 22:06.
10. Re: bearings question
(Original post by TenOfThem)
i get
298.6 and 171.4
the book has answers 171.4 and 328.6
11. Re: bearings question
(Original post by zoxe)
the book has answers 171.4 and 328.6

That is what I get
12. Re: bearings question
13. Re: bearings question
If AB is a straight line then theta is 110 isn't it? Surely

Theta being the angle marked in the diagram.
Last edited by SubAtomic; 09-07-2012 at 22:12.
14. Re: bearings question
(Original post by SubAtomic)
If AB is a straight line then theta is 110 isn't it? Surely
It would be if C1 were North of B but it isn't
15. Re: bearings question
(Original post by TenOfThem)
It would be if C1 were North of B but it isn't
I don't understand your working, could you explain?

Also the diagram is from the solutions page, I've just added the red parts, i.e my working.
Last edited by zoxe; 09-07-2012 at 22:19.
16. Re: bearings question
(Original post by TenOfThem)
It would be if C1 were North of B but it isn't
Based on that diagram in the OP theta represents 110? If the plane is traveling at a bearing 070?

Or is it the case in text books that theta can represent different values even without being written
Last edited by SubAtomic; 09-07-2012 at 22:18.
17. Re: bearings question
(Original post by TenOfThem)
It would be if C1 were North of B but it isn't
Okay with your diagram it's so simple, how did you know C1 and C2 were drawn that way?
18. Re: bearings question
Might help (I used "t" for theta).
Attached Thumbnails

19. Re: bearings question
(Original post by ghostwalker)
Might help (I used "t" for theta).
same as tenofthem, how did you know the position of C1 and C2?
20. Re: bearings question
So the diagram in the OPs text book is completely wrong?