A triangle has sides A, B, and C. Sides A and B are of lengths #4# and #9#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?

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Answer 1 · 2018-03-13T07:41:50

#c=11.2#

Well, this is a classic use of the cosine rule

#c^2=a^2+b^2-2abcos(C)#

#c^2=(4)^2+(9)^2-2(4)(9)cos((5pi)/8)#

#c^2=16+81-72(-0.382683)#

#c^2=124.553#

#c=sqrt(124.553)#

#c=11.2#