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
Tony B
Apr 1, 2016

C= 3sqrt(13)

Explanation:

You use the Cosine rule for this

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

Tony BTony 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.

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