How to find the angle of CAD ?

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1 Answer
CW
Oct 23, 2017

see explanation.

Explanation:

#(i) angleACB=180-50-48=82^@#
By the law of sines
#(AB)/sin82=(AC)/sin48, => AB=55*sin82/sin48~~73.29m#

#(ii)# use the law of cosines,
#CD^2=AD^2+AC^2-2*AD*AC*cosangleCAD#
#=> cosangleCAD=(70^2+55^2-25^2)/(2xx70xx55)#

#=> angleCAD=cos^-1((70^2+55^2-25^2)/(2xx70xx55))~~18.55^@#

#(iii)# area of #DeltaABC=1/2*AB*AC*sinangleCAB#
#=1/2*73.29*55*sin50~~1543.94 " m"^2#

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