A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #9#, respectively, and the angle between A and B is #(3pi)/4 #. What is the length of side C?

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Answer 1 · 2016-07-10T10:42:36

#C=10.51#

Since, by the Carnot theorem:

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

in this case

#C=sqrt(2^2+9^2-2*2*9*cos3pi/4#

#C=sqrt(4+81-36*(-sqrt(2)/2))#

#C=sqrt(85+18sqrt(2))#

#C=10.51#