A triangle has sides A, B, and C. Sides A and B are of lengths #3# and #7#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

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Answer 1 · 2017-07-08T17:13:58

The length is #=4.65u#

The side #A=3#

The side #B=7#

The angle between #A# and #B# is #=1/6pi#

We apply the cosine rule to the triangle

#C^2=A^2+B^2-2ABcos hat(C)#

#=3^2+7^2-2*3*7*cos(1/6pi)#

#=9+49-42cos(1/6pi)#

#=21.6#

#C=sqrt21.6=4.65#