A triangle has sides A, B, and C. The angle between sides A and B is #(7pi)/12#. If side C has a length of #2 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-02-25T07:23:50

#A=2sqrt3-4#

You would apply the sine theorem to find the length of side A:

#A/sin hat(BC)=C/sin hat (AB)#

Then

#A=C*sin hat(BC)/sin hat(AB)#

#A=(2*sin(pi/12))/sin((7pi)/12)#

#=(2*((sqrt2-sqrt6))/cancel4)/((sqrt2+sqrt6)/cancel4)#

#=(2(sqrt2-sqrt6)^2)/((sqrt2+sqrt6)(sqrt2-sqrt6))#

#=(2(sqrt2-sqrt6)^2)/(2-6)#

#=(cancel2(2+6-2sqrt12))/-cancel4^2#

#=-(cancel8^4-cancel2sqrt12)/cancel2#

#=sqrt12-4#

#=2sqrt3-4#