A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3#. If side C has a length of #6 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2018-02-25T05:16:36

Length of side #color(green)(a = (c * sin A) / sin C ~~ 6.4#

Length of side #color(blue)(b = (c * sin B) / sin C ~~ 6.869#

#hat C = pi/3, hat A = (3pi)/8, c = 6#

Third #hat B = pi - ((3pi)/8) - pi / 6 = (11pi)/24#

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Applying law of sine,

#color(green)(a = (c * sin A) / sin C = (6 * sin ((3pi)/8)) / sin ((pi)/3) ~~ 6.4#

#color(blue)(b = (c * sin B) / sin C = (6 * sin ((11pi)/24)) / sin (pi/3) ~~ 6.869#