Question 1203473
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The answer is approximately <font color=red>684.864918 km</font>. I rounded to 6 decimal places. Feel free to round however else your teacher instructs. I have confirmed this answer with GeoGebra.


Tutor ikleyn has a value (684.864691) close to what I got. However there's slight rounding error. The "684.864" portions match up at least.


Tutor theo has at least one error in his calculations. The good news is that 687.4045186 is somewhat close to 684.864918


I'll explain why the formula ikleyn uses works. 


The four key bearing angles to memorize are:
000° = north
090° = east
180° = south
270° = west
Check out the diagram below. 
Basically we start aiming north. Then rotating clockwise will increase the bearing angle. 


So let's say the bearing is 050° and we move 100 km along this bearing. 
We move 100 km along the red arrow.
*[illustration Screenshot_266.png]


We want to know how far north we are from the origin. 
Thus we want to find the vertical leg of this right triangle marked in red.
cos(angle) = adjacent/hypotenuse
cos(50) = adjacent/100
adjacent = 100*cos(50)


Therefore the north-south displacement for this example is 100*cos(50) = 64.27876 km approximately.


In general if you move r units along bearing theta degrees, then r*cos(theta) units is the north-south displacement. 
Negative displacement means we move south, while positive displacements move us north.


This idea can then be applied many times to chain together multiple movements. 
That is how ikleyn ended up with the formula: 450*cos(320°) + 130*cos(350°) + 330*cos(50°) 
Make sure your calculator is in degree mode. A quick check could be something like cos(60°) = 0.5 which you should have memorized.


Feel free to ask any further questions if you're still stuck.
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