A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is #(pi)/12# and the angle between B and C is # (2pi)/3#. What is the area of the triangle?
Formula for area of a triangle in terms of its two sides is half the product of two sides multiplied by sine of the angle between the two sides.
Here we have sides A and B, but we do not know the angle between them.
Fr this, as sum of internal angles of a triangle is
third angle is
Area of triangle is