A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 8, respectively. The angle between A and C is #(pi)/4# and the angle between B and C is # (pi)/3#. What is the area of the triangle?

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Answer 1 · 2018-06-03T10:20:17

Since it doesn’t satisfy the law of Sines, we can’t form a triangle with the given measurements

#a = 12, b = 8, hat A = pi/3, hat B = pi/4#

As per the Law of Sines,

#a / sin A = b / sin B = c / sin C#

#a / sin A = 12 / sin (pi / 3) = 8sqrt3#

#b / sin B = 8 / sin (pi/4) = 8sqrt2#

Since it doesn’t satisfy the law of Sines, we can’t form a triangle with the given measurements