A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/6#. If side C has a length of #9 # and the angle between sides B and C is #(7pi)/12#, what are the lengths of sides A and B?

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Answer 1 · 2018-02-26T14:24:19

Length of sides #color(brown)(a = 17.3867, b = 12.7279)#

Given : #hat C = pi/6, hat A = (7pi)/12, c = 9#

#hat B = pi - (7pi)/12 - pi / 6 = pi / 4#

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Applying law of sines,

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

#b = (c sin B) / sin C = (9 * sin (pi/4)) / sin (pi/6) = 12.7279#

#a = (b sin A) / sin B = (12.7279 * sin ((7pi)/12)) / sin (pi/4) = 17.3867#