Question 388061
Convert both displacements to x,y coordinates. 
Positive x is East. 
Positive y is North.
Angle is measured CCW from x-axis.
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{{{D[BC]}}}=({{{500*cos(90+44)}}},{{{500*sin(90+44)}}})
{{{D[CA]}}}=({{{720*cos(180+beta)}}},{{{720*sin(180+beta)}}})
where 
{{{720*sin(beta)=500*sin(46)}}}
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{{{drawing(300,300,-10,10,-10,10,
line(3,0,0,5),
line(0,5,-7,0),
line(-7,0,3,0),
line(3,0,3,5),
locate(1.75,3,44),
locate(3,0,B),
locate(0,6.5,C),
locate(-7,0,A),
line(0,5,-7,5),
blue(line(0,0,0,5)),
locate(-3,4.6,beta),
line(-0.5,0,-0.5,0.5),
line(-0.5,0.5,0.5,0.5),
line(0.5,0.5,0.5,0),
locate(1,1,46))}}}
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{{{720*sin(beta)=500*sin(46)}}}
{{{sin(beta)=(500/720)*sin(46)}}}
{{{sin(beta)=0.4995}}}
{{{beta=30}}}
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{{{D[BC]}}}=({{{500*cos(134)}}},{{{500*sin(134)}}})
{{{D[BC]}}}=({{{-347.3}}},{{{359.7}}})
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{{{D[CA]}}}=({{{720*cos(210)}}},{{{720*sin(210)}}})
{{{D[CA]}}}=({{{-623.5}}},{{{-360}}})
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{{{D}}}={{{D[BC]+D[CA]}}}
{{{D}}}=({{{-347-623}}},{{{360-360}}})
{{{D}}}=({{{-970}}},{{{0}}})
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The plane is 970 km from the starting point due west.