A triangle has sides A, B, and C. Sides A and B are of lengths #9# and #12#, respectively, and the angle between A and B is #pi/3#. What is the length of side C?

1 Answer
Apr 1, 2016

Answer:

#C= 3sqrt(13)#

Explanation:

You use the Cosine rule for this

Note that #cos(pi/3) -> cos(60^o) = 1/2#

Tony B

For the notation of this question and my diagram.

Cosine rule#-> C^2=A^2+B^2 - 2ABcos( a)#

#=> C^2=9^2+12^2 - 2(9)(12)(1/2)#

#C^2 =81+144-108 = 117#

#=>C^2=sqrt(3^3xx13)#

#=>C= 3sqrt(13)#

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Comment:

I always understood that the standard practice of labelling was that capital letters were used for the vertices (angles) and that small letters were used for the sides.