A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (7pi)/24#. What is the area of the triangle?
Call the angle opposite side A as
and similarly the angle opposite Side B as
and the angle opposite Side C as
We are told (among other things) that:
The Sine Law tells us
Evaluating we get:
We now have the lengths of the three sides and can apply Heron's Formula: