A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 6, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (13pi)/24#. What is the area of the triangle?
The angles in a triangle add up to
so the angle between sides A and B is 4
The area of a triangle is 1/2 x A x B x sin (angle between them)
Or 1/2 x 8 x 6 x sin
The ratio of the sides is 1;2:
Sin 30 =1/2
The area of the triangle is 1/2 x 8 x 6 x 1/2 =12