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M1 Vectors

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 attempted it but my answer is not the same as the solution given. I don't understand even after looking over the solution so could someone explain how to do this question. I got the first part 171 bearing but i did it differently to the solution and second part I got 328 instead of 323.6.
http://pmt.physicsandmathstutor.com/download/Maths/A-level/M1/Solutionbank-Heinemann/M1%20Chapter%206.pdf - Pg 6, EX A Q6.

Thanks.
Original post by Outofthisworld
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 attempted it but my answer is not the same as the solution given. I don't understand even after looking over the solution so could someone explain how to do this question. I got the first part 171 bearing but i did it differently to the solution and second part I got 328 instead of 323.6.
http://pmt.physicsandmathstutor.com/download/Maths/A-level/M1/Solutionbank-Heinemann/M1%20Chapter%206.pdf - Pg 6, EX A Q6.

Thanks.


You are looking for the black angle (as one possibility) which is your bearing. This should be clear to you that this is indeed the bearing of flight from BB to C2C_2 as the angle is measured from the north line (imagine the north line is B to C1 here, though it's not actually. Their diagram makes it a pain to draw on the north line, so it'll make do). You should be aware of 'corresponding' angles from GCSE, so the red angle and the blue angle above the letter B are corresponding angles, hence they are the same. You should also be aware of 'vertically opposed' angles, which is precisely what both of the blue angles are to each other, hence we have the other 70 degrees below the letter B.

To obtain the black angle, we start from the north line and go 180 degrees to reach the dashed blue line, then we go another 70 to reach the line AB. Hence the bearing of A from B is 180+70. But, it is also the same as (black angle)+(theta). You know what theta is, so thats where their C2C_2 bearing comes from.

Similar analysis is done for the second option, though I do agree that the answer is around 328 rather than 323

(edited 6 years ago)

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