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

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Answer 1 · 2016-12-06T15:51:51

Let

#alpha->"angle between B and C"=pi/3#

#beta->"angle between A and C"=pi-(pi/3+pi/12)=(7pi)/12#

#gamma->"angle between B and A"=pi/12#

#"side " B=7#

By properties of triangle

#C/singamma=B/sinbeta#

#C=(Bsingamma)/sinbeta#

Now area of the triangle

#Delta=1/2BCsinalpha#

#=>Delta=1/2xxBxx(Bsingamma)/sinbetaxxsinalpha#

#=1/2xx7^2xx(sin(pi/12)sin(pi/3))/sin((7pi)/12)#

#~~5.685" squnit"#