A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 15, 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?
We know that:
and as the sum of the internal angles of a triangle always equals
We can use this to determine
Then we can use Eron's formula to calculate the area from the sides:
As the angles are not such as the sine is immediately known we can use approximate values or do a bit of computation using trigonometric formulas.