A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 3, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-03-30T11:37:50

The area of the triangle is # 2.33(2dp) # sq.unit.

The angle between sides #A and C# is #/_b=(13pi)/24 = (13*180)/24= 97.5^0#
The angle between sides #B and C# is #/_a=(3pi)/8 = (3*180)/8= 67.5^0#

The angle between sides #A and B# is #/_c=180-(97.5+67.5)= 15^0#

We know sides #A=6 , B=3# and their included angle #/_c= 15^0#

The area of the triangle is #A_t=1/2*A*B*sinc=1/2*6*3*sin15=9*sin15~~ 2.33(2dp) #sq.unit [Ans]