A triangle has sides A, B, and C. The angle between sides A and B is #(7pi)/12#. If side C has a length of #19 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-07-23T09:51:56

The length is #=5.09u#

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The angles are

#hatA=1/12pi#

#hatC=7/12pi#

Therefore,

#hatB=pi-(1/12pi+7/12pi)=pi-8/12pi=4/12pi=1/3pi#

The sides are

#c=19#

We apply the sine rule to the triangle

#a/sin hatA=c/sin hatC#

#a=c*sin hatA/sin hat C#

#=19*sin(1/12pi)/sin(7/12pi)#

#=5.09#