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 isA_t= (A*B*sinc)/2=(8.2*3*sin30)/2=6.15(2dp)sq.unit[Ans]

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