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 #15 # 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 · 2017-04-11T06:06:57

#A = 28.978#
#B = 21.213#

Angle of #A = (7 pi)/12, C = pi/6#, therefore angle of #B = pi - (7 pi)/12 -pi/6 = (3 pi)/12#

we use a formulae, # A / sin A = B / sin B = C / sin C#

#A / sin A = C / sin C#

#A / sin ((7 pi)/12) = 15 / sin (pi/6)#

#A = 15 / sin (pi/6) * sin ((7 pi)/12) =15 / 0.5 * 0.966 = 28.978#

#B / sin B = C / sin C#

#B / sin ((3 pi)/12) = 15 / sin (pi/6)#

#B = 15 / sin (pi/6) * sin ((3 pi)/12) = 15/0.5 *0.707= 21.213#