A triangle has sides A, B, and C. Sides A and B are of lengths #9# and #17#, respectively, and the angle between A and B is #(7pi)/8 #. What is the length of side C?

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Answer 1 · 2016-07-20T17:18:00

#C~=25.5483#.

We use Cosine-Rule, which, in our case, states that,

#C^2=A^2+B^2-2ABcos(/_(A,B))#

#=81+289-2xx9xx17cos(7pi/8)#

#=370-306cos(pi-pi/8)#

#=370-306(-cospi/8)..................... [cos(pi-theta)=-costheta]#

#370+306cos(22^@30')#

#370+306(0.9239)#

#370+282.7134=652.7134#

#:. C=sqrt652.7134~=25.5483#.