A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 4, 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?
Let us plot the triangle, and let us find its area using trigonometry.
First of all, our triangle is similar to the next one:
The area of the above triangle can be calculated by:
i.e. we must multiply two sides and the sine of the angle between them.
We know A and B sides, but we do not know the angle. We may calculate it by knowing that, for any triangle with angles