A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #1#, respectively, and the angle between A and B is #(7pi)/8 #. What is the length of side C?

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Answer 1 · 2018-02-12T21:32:02

#c=sqrt(48.087)~~6.934# ( 3 .d.p.)

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The Cosine Rule:

#color(red)bb(a^2=b^2+c^2-2bc*cosA)#

Since we are looking for side c we rearrange this to get:

#c^2=a^2+b^2-2ac*cosC#

Substituting given values:

#c^2=(6)^2+(1)^2-2(6)(1)*cos((7pi)/8)#

#c^2=36+1-(12*cos((7pi)/8))#

#c^2=37-(-11.087)#

#c^2=48.087#

#c=sqrt(48.087)~~6.934# ( 3 .d.p.)