A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/3, the angle between sides B and C is (5pi)/12, and the length of B is 2, what is the area of the triangle?

1 Answer
Binayaka C.
Jun 10, 2016

Area of the triangle is 2.36(2dp) sq units

Explanation:

The angle between sides A and B is /_C=pi/3 = 180/3 = 60^0
The angle between sides B and C is /_A= (5pi)/12 = (5*180)/12= 75^0
The angle between sides C and A is /_B=180-(60+75) = 45^0
B=2 (given) Applying sine law we get A/sinA=B/sinB or A=2*sin75/sin45=2.73 Now A=2.73 ; B=2 and their included angle /_C=60^0 So area of the triangle is a*b*sinC/2= 2.73*2*sin60/2=2.36(2dp)sq units [Ans}

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