Question

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?

Answer 1

`C= 3sqrt(13)`

Explanation:

You use the Cosine rule for this

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

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)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.