A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #5#, respectively, and the angle between A and B is #pi/4#. What is the length of side C?

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Answer 1 · 2016-09-27T21:16:01

#:. C=~~3.855.#

We use the Cosine-Rule for #DeltaABC#, which states,

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

where, by "#/_(A,B)#, we mean the angle btwn. sides #A & B.#.

#:. C^2=2^2+5^2-2*2*5cos(pi/4)#

#=29-20(1/sqrt2)=29-10sqrt2#

#~~29-10(1.414)=29-14.14=14.86#

#:. C~~3.855#