A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 4, respectively. The angle between A and C is #(pi)/12# and the angle between B and C is # (2pi)/3#. What is the area of the triangle?

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Answer 1 · 2016-10-02T10:09:30

Let angle beween A and C #=beta=pi/12#

Angle beween B and C #=alpha=(2pi)/3#

So angle beween A and B #=gamma=pi-pi/12-(2pi)/12=pi/4#

Again sides #A=9 and B=4#

The area of the triangle

#Delta=1/2xxAxxBxxsingamma#

#=>Delta=1/2xx9xx4xxsin(pi/4)#

#=18xx1/sqrt2=9sqrt2squnit#