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

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Answer 1 · 2018-02-17T03:38:59

Area of triangle #A_t = (1/2) * a * b * sin C = color(red)(2.5758#

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#hatC = pi/3, hat A = (5pi)/12, b = 2#

#hatB = pi - (5pi)/12 - (pi/3) = pi/4#

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

#a = (2 * sin ((5pi)/12)) / sin (pi/4) = 2.2307#

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

#A_t = (1/2) * 2.2307 * 2 sin (pi/3) = color(red)(2.5758#