A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (5pi)/8#. What is the area of the triangle?
The area is
The area is one half the product of two sides times the sine of the angle between them.
Here we are given two sides but not the angle between them, we are given the other two angles instead. So first determine the missing angle by noting that the sum of all three angles is
Then the area of the triangle is
We have to compute
Then the area is given by: