A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #12 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2016-02-16T08:15:17

#a=3.5863# units

Given Two Angles and a side opposite one of them. Use Sine Law

Given: Angle #C=(2pi)/3# and angle #A=pi/12#
side #c=12#

Solve for side #a#:

From Sine Law: #a/sin A=c/sin C#

#a=(c*sin A)/sin C=(12*sin(pi/12))/sin ((2pi)/3)#

#a=3.5863#

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