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]

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(13pi)/24 and the angle between B and C is (3pi)/8 (3pi)/8. What is the area of the triangle?