A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 7, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (11pi)/24#. What is the area of the triangle?
Area = (½) * 3 * 2.12= 3.18 (repeated from another post)
Triangle area = (1/2)(base)(height)
Take side B to be the base, then h is the sin of the angle between sides B and A times the length of B.
That angle is (π - 7π/24 – 11π/24) = 6π/24
sin C = h/B ; sin (6π/24) = h/3
h = sin(0.785) * 3 ; h = 0.707 * 3 = 2.12
Area = (½) * 3 * 2.12= 3.18