A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/3#, the angle between sides B and C is #(7pi)/12#, and the length of B is 7, what is the area of the triangle?

1 Answer
Deepak G.
Aug 7, 2016

#=79.16#

Explanation:

This is a triangle where side #B=7# is opposite of the
Angle [#pi-(pi/3+7pi/12)]=pi-11pi/12=pi/12#
Therefore
#B/sin(pi/12)=C/sin(pi/3)#
or
#7/sin(pi/12)=C/sin(pi/3)#
or
#C=7sin(pi/3)/(sinpi/12)#
or
#C=7(3.34)#
or
#C=23.42#
#Height # of the triangle is #=7sin(pi-7pi/12)=7sin (5pi/12)=6.76#
Therefore
Area of the triangle#=1/2(C)(Height)#
#=1/2(23.42)(6.76)#
#=79.16#

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