Minimizing and optimization related rate problem

[Alphax]

I would like to ask for help solving this problem. I've been at this problem for a few hours without making any progress.

There is a picture of the problem attached in this thread.

So, the question is what is the length of side 'X' used in order to get the shortest possible length for side 'R'. The given value for the triangle are 14 cm on one side and a 40° angle.

what are the steps in approaching the problem?

 

[Alphax]

Maybe someone can point to me a source on the internet to understand the concept a bit more?

 

[PlayingCatchUp]

http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx

I think you can make an equation with the sine law for R but it will still have an unknown theta in it.
You know the unknown angle must be less than 140. R = 14*sin40/θ.