A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 2, respectively. The angle between A and C is #pi/4# and the angle between B and C is # pi/3#. What is the area of the triangle?

1 Answer
Jul 10, 2017

Area of triangle is #7.73# sq.unit

Explanation:

Angle between sides #A and C# is #/_b=pi/4=180/4=45^0#
Angle between sides #B and C# is #/_a=pi/3=180/3=60^0#
Angle between sides #A and B# is #/_c=180-(60+45)=75^0#

Now we know sides #A , B# and their included angle #/_c#

Sides #A= 8 , B=2, /_c=75^0#

Area of triangle is #A_t= (A*B*sinc)/2 = (8*cancel2*sin 75)/cancel2 = 8*sin75# or

#A_t ~~=7.73(2dp) #sq.unit

Area of triangle is #7.73(2dp) #sq.unit [Ans]