Question #8e263

1 Answer
CW
Jan 6, 2018

see explanation

Explanation:

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set your calculator mode in radians
a) use the law of cosines to find #angleBAC#,
#BC^2=AB^2+AC^2-2*AB*AC*costheta#,
#=> theta=cos^-1((8^2+7^2-6^2)/(2*8*7))=0.813# radians
b) area of #DeltaABC#
#A_(ABC)=1/2*AB*AC*sintheta=1/2*8*7*sin0.813=20.338 " cm"^2#,
c) area of sector #AXY#,
#A_(AXY)=1/2*r^2*theta=1/2*5^2*0.813=10.163 " cm"^2#,
d) area of #XBCY#
#A_(XBCY)=A_(ABC)-A_(AXY)#
#=20.338-10.163=10.175 " cm"^2#

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