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Answer 1 · 2018-01-25T12:50:27

#BC~~108m##

First, we need to find the distance from the base to points B and C.

#tantheta=O /A#

#A=O /tantheta#

#AB=40/tan20~~110m#

#AC=40/tan12~~188m#

The bearings can be shown approximately as:
enter image source here

#/_CAB=18+(360-(18+330))=18+(360-348)=18+12=30^circ#

The cosine rule tells us that:
#c=sqrt(a^2+b^2-2abcosC)#

#c=sqrt(110^2+188^2-2(110*188)cos30)#

#color(white)(c)=sqrt(12100+35344-2(20680)sqrt(3)/2)#

#color(white)(c)=sqrt(12100+35344-20680sqrt(3))#

#color(white)(c)~~sqrt(11625.1893)#

#color(white)(c)~~107.8m#

#color(white)(c)~~108m#