A triangle has sides A, B, and C. Sides A and B are of lengths #8# and #3#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?

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Answer 1 · 2018-07-12T16:30:01

#c=sqrt(73-48sqrt(2+sqrt(2))#

Using the Theorem of cosines

#c^2=a^2+b^2-2ab\cos(\gamma)#

with

#a=8,b=3#

and #cos(pi/8)=sqrt(2+sqrt(2))/2#

we get

#c^2=64+9-2*3*8*cos(pi/8)#

#c=sqrt(73-48sqrt(2+sqrt(2))#