Question 1203473
.
A plane flies on a true bearing of 320° for 450 km. 
It then flies on a true bearing of 350° for 130 km 
and finally on a true bearing of 050° for 330 km. 
How far north of its starting point is the plane?
~~~~~~~~~~~~~~~~~~



        While solving this problem,  I will assume that the Earth surface is flat :)



<pre>
In this problem, all angles are counted from the Northern direction (from y-axis) 
clockwise.


The question asks "how far North is the plane from its starting point?"


To answer this question, it is enough to add algebraically all projections 
of partial displacements on y-axis.  This formula does it


    how far North = 450*cos(320°) + 130*cos(350°) + 330*cos(50°) = 

                  = 450*0.7660444 + 130*0.9848077 + 330*0.642787 = 684.864691 kilometers.


    +---------------------------------------------------------+
    |      I use cosine function, since in this problem       |
    |   it provides projections of displacements on y-axis.   |
    +---------------------------------------------------------+


<U>ANSWER</U>. 684.86 kilometers, rounded.
</pre>

Solved &nbsp;(in a way as it is expected and as it &nbsp;SHOULD &nbsp;be done).



====================



By the way, for your better understanding, &nbsp;the precision in this problem 
should not be smaller than the size of the plane &nbsp;(which is tens of meters),
otherwise the answer is illogical and makes no sense


When the other tutor, &nbsp;while retelling my solution, &nbsp;reproaches me for inaccuracy in one unit
in the last 6th decimal place &nbsp;(which corresponds to one millimeter) &nbsp;in the intermediate calculation, 
(before I made my final rounding), &nbsp;it is just out of common sense.



\\\\\\\\\\\\\\\\\\



The formula, which I use, is a standard formula from adding vectors on a coordinate plane.

This formula is a prerequisite for solving such problems. So, at normal teaching process, 
you should learn this formula before you get this problem as an assignment.

It is why I do not repeat what you should know from your teacher/professor or from your textbook.