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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

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Reply 1

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

Reply 2

zoxe

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

Reply 3

TenOfThem

Sorry, yes the 78.6 is right (I used 70 instead of 60 because of your diagram :frown:

)

Reply 4

TenOfThem

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

Reply 5

ghostwalker

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.

Reply 6

zoxe

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.

Reply 7

zoxe

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.

Reply 8

TenOfThem

i get
328.6 and 171.4

(edited 11 years ago)

Reply 9

zoxe

Original post by TenOfThem

i get
298.6 and 171.4

the book has answers 171.4 and 328.6

Reply 10

TenOfThem

Original post by zoxe

the book has answers 171.4 and 328.6

yes, sorry a mis read

That is what I get

If AB is a straight line then theta is 110 isn't it? Surely :s-smilie:

Theta being the angle marked

\theta

in the diagram.

(edited 11 years ago)

Reply 13

TenOfThem

Original post by SubAtomic

If AB is a straight line then theta is 110 isn't it? Surely :s-smilie:

It would be if C1 were North of B but it isn't

Reply 14

zoxe

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.

(edited 11 years ago)

Reply 15

SubAtomic

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