Do not use a calculator in this question.

In this question, all lengths are in centimetres.

A triangle \(ABC\) is such that angle \(B=90^\circ\), \(AB=5\sqrt3+5\) and \(BC=5\sqrt3-5\).

(i) Find, in its simplest surd form, the length of \(AC\).

(ii) Find \(\tan BCA\), giving your answer in the form \(a+b\sqrt3\), where \(a\) and \(b\) are integers.