A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/12# and the angle between sides B and C is #pi/6#. If side B has a length of 1, what is the area of the triangle?

1 Answer
Binayaka C.
Nov 14, 2016

The area of the triangle is #1/4 sq.unit#

Explanation:

The angle between sides #A and B# is #/_c=(5pi)/12=(5*180)/12=75^0#.

The angle between sides #B and C# is #/_a=pi/6=180/6=30^0#

The angle between sides #A and C# is #/_b=180-(75+30)=75^0#

#/_b= /_c=75^0#. So it is an isocelles triangle , having opposite sides equal. So #B=C=1# and their included angle #/_a=30^0#

Hence the area of the triangle is #A_t=(B*C*sin a)/2=(1*1*sin30)/2=1/4 sq.unit#[Ans]

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