A triangle has sides A, B, and C. If the angle between sides A and B is #(5pi)/12#, the angle between sides B and C is #pi/3#, and the length of B is 2, what is the area of the triangle?

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Answer 1 · 2018-02-17T03:52:19

#A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366#

Given : #b = 2, hatA = pi/3, hatC = (5pi)/12#

#hatb = pi - (pi/3 + (5pi)/12) = pi/4#

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

#a = (b * sin A) / sin B = (2 * sin (pi/3)) / sin ((pi/4) = 2.4495#

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

#A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366#