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A triangle has sides A, B, and C. The angle between sides A and B is #(7pi)/12# and the angle between sides B and C is #pi/12#. If side B has a length of 72, what is the area of the triangle?

1 Answer

Jun 3, 2018

Area of the triangle #A_t = color(crimson)(748.32)#

Explanation:

#hat A = pi/12,hat C = (7pi):12, hat B = pi/3, b = 72#

Law of Sines #a/sin A = b / sin B = c / sin C#

#Area = A_t = (1/2) a b sin C#

#a = (b sin A) / sin B = (72 * sin (pi/12)) / sin (pi/3) = 21.52#

#A_t = (1/2) * 21.52*72*sin((7pi)/12) = color(crimson)(748.32)#

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