Well, there's the cosine rule: a²=b²+c²-2bcCosA, meaning that x²=14²+15²-2*14*15*cos55, so x=√(14²+15²-2*14*15*cos55)=13.4, to one decimal place.
You could also cut it in half, but that involves calculating three more lengths before you're allowed to find x, so I think that this way's actually easier.