A triangle has sides A, B, and C. The angle between sides A and B is #pi/3# and the angle between sides B and C is #pi/12#. If side B has a length of 3, what is the area of the triangle?

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Answer 1 · 2017-07-10T06:21:04

The area is #=1.04u^2#

The third angle of the triangle is

#=pi-(pi/3+pi/12)=pi-5/12pi=7/12pi#

We apply the sine rule to the triangle

#A/sin(1/12pi)=B/sin(7/12pi)#

#A/sin(1/12pi)=3/sin(7/12pi)=3.11#

#A=3.11*sin(1/12pi)=0.8#

The area of the triangle is

#=1/2ABsin(1/3pi)=0.5*0.8*3*sin(1/3pi)=1.04#