A triangle has sides A, B, and C. The angle between sides A and B is #pi/6# and the angle between sides B and C is #pi/12#. If side B has a length of 1, what is the area of the triangle?

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Answer 1 · 2017-08-07T12:06:42

Area of the triangle is #0.09# sq. unit.

The angle between sides #A and B # is #/_c= pi/6=180/6= 30^0#.

The angle between sides #B and C # is #/_a= pi/12=180/12= 15^0#

The angle between sides #C and A# is #/_b= 180-(30+15)=135^0#

#B=1 # . Applying sine law we get # A/sina = B/sinb #

# :. A = B * (sina/sinb) = 1 * sin15/sin135 =0.366#

Now we have #A = 0.366 , B =1 # and their icluded angle

#c=30^0 #:. Area of the triangle is #A_t = (A*B*sinc)/2 # or

# A_t= (1*0.366*sin30)/2 = (0.366 * 1/2)/2 ~~ 0.09# sq. unit Ans]