The triangle $ABC$ is such that $AB$ has length $x,$ $BC$ has length $x-1$ and $CA$ has length $2$.

Given that the angle at $B$ is ${30}^{\circ },$ find the value of $x,$ giving your answer to three significant figures.

You should end up with a quadratic in terms of $x.$ It might look a bit scary, but use the quadratic formula carefully and it will work out.