A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 6, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-07-21T15:38:21

The area is #=13.5u^2#

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The lengths of the sides are

#a=9#

#b=6#

The angles are

#hatA=3/8pi#

#hatB=11/24pi#

Therefore,

#hatC=pi-(3/8pi+11/24pi)=pi-20/24pi=1/6pi#

The area of the triangle is

#area=1/2ab sin (hatC)#

#=1/2*9*6+sin(pi/6)#

#=1/2*9*6*1/2=13.5u^2#