A triangle has sides A, B, and C. Sides A and B are of lengths #3# and #2#, respectively, and the angle between A and B is #pi/4#. What is the length of side C?

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Answer 1 · 2016-02-09T13:00:04

#=2.124#

Consider the diagram:

enter image source here

Use cosine rule:

#color(orange)(C^2=A^2+B^2-(2ABcosc)#

Here #A=3,B=2#

Remember #color(green)(pi=180^circ#

#rarrC^2=3^2+2^2-(2(3)(2)cos(pi/4))#

#rarrC^2=9+4-(12cos45^circ)#

#rarrC^2=13-(12(sqrt2/2))#

#rarrC^2=13-(8.485..)#

#rarrC^2=4.515#

#rarrC=sqrt4.515#

#color(blue)(C~~2.124..#