A triangle has sides A,B, and C. If the angle between sides A and B is #(3pi)/4#, the angle between sides B and C is #pi/12#, and the length of B is 9, what is the area of the triangle?

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Answer 1 · 2018-05-24T14:32:32

Area of triangle #color(maroon)(A_t = 14.83# sq units

Given : #hat A = pi/12, hat C = (3pi)/4, b = 9#

#hat B = pi - pi/12 - (3pi)/4 = pi/6#

#a / sin A = b / sin B #

#a = (b sin A) / sin B = (9 * sin (pi/12)) / sin (pi/6)#

#a = 4.66#

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

#A_t = (1/2) * 4.66 * 9 * sin ((3pi)/4)#

#A_t = 14.83# sq units