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trigonometry help

A hiker walks from A to B on a bearing of 060°. After 7km he reaches Band then walks a further 12km on a bearing of140 to point Ca) What is the distance from A to Cb) What is the bearing of C from A

I got 14.9km as the distance, which is correct but the bearing I got 112.5km. I used the Sine Rule and added angle opposite 12km to 60degrees. The answer should be 292.6degrees.
Reply 1
Avatar for marmbite
marmbite
9
The answer you got of 112.5° for the bearing of C from A is correct, I did it a slightly different way and got the same answer. I have also realised that it can't be 292.6° as when I drew it out this would have been in the wrong direction.
On the other hand, the bearing of A from C is 292.6°.
I suspect that you got the correct answer for C from A and so I think you have the skills to work out A from C at 292.6.
However, if you need a nudge, just remember to draw the question out (I find this a lot easier than trying to visualise it) and remember that the bearings can be co-interior/allied angles. Also don't forget to apply the most basic rules, you may not need anything complex.

I have also shown a full solution in the spoilers if you wish to see.

Spoiler




Spoiler




(sorry the second part isn't so clear, I couldn't get the scanned version to upload so I had to use a photograph)

(edited 9 years ago)
triginometry problem part 1.jpg493.6KB
trigomometry promblem part 2.jpg192.9KB

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