A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/6#, the angle between sides B and C is #(3pi)/4#, and the length of side B is 3, what is the area of the triangle?

1 Answer
Binayaka C.
Aug 18, 2016

Area of the triangle is #6.15(2dp)# sq.unit.

Explanation:

The angle between sides A and B is #/_c= pi/6=30^0#
The angle between sides B and C is #/_a= 3*pi/4=135^0#
The angle between sides C and A is #/_b= (180-(30+135)=15^0#
Using sine law we get #A/sina=B/sinb or A= 3*(sin135/sin15)=8.2#
Now we know two sides A & B and their included angle#/_c :.#
Area of the triangle is#A_t= (A*B*sinc)/2=(8.2*3*sin30)/2=6.15(2dp)#sq.unit[Ans]

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