A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 4, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-11-05T11:29:19

Area of the triangle is #3sqrt3# sq.unit.

Angle between Sides # A and C# is # /_b= (5pi)/24#

#=(5*180)/24=37.5^0#

Angle between Sides # B and C# is # /_a= pi/8=180/8=22.5^0 :.#

Angle between Sides # A and B# is

# /_c= 180-(37.5+22.5)=120^0#

We know sides #A=3 , B=4# and their included angle #/_c=120^0#

Area of the triangle is #A_t=(A*B*sinc)/2= (3*4*sin120)/2#

#= 6 sin120 =6 *sqrt3/2 =3sqrt3# sq.unit