A triangle has sides A, B, and C. The angle between sides A and B is #(3pi)/4# and the angle between sides B and C is #pi/12#. If side B has a length of 22, what is the area of the triangle?

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Answer 1 · 2018-03-07T03:27:31

Area of the #Delta ABC# #color(indigo)(A_t = 88.5781# sq units

Third angle #hat B = pi - hat A - hat C = pi - pi / 12 - (3pi) / 4 = pi / 6#

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#22 / sin (pi / 6 )= a / sin (pi / 12) = c / sin ((3pi) /4)#

#c = (22 * sin ((3pi)/4)) / sin (pi/ 6) = (22 * (1/sqrt2)) / (1/2) = 22 sqrt 2#

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Using SAS formula to calculate the area of the triangle,

#A_t = (1/2) b c sin A = (1/2) * 22 * 22 sqrt 2 * sin (pi / 12)#

#color(indigo)(A_t = 88.5781# sq units