In this question all lengths are in centimetres.

The diagram shows triangle \(ABC\) with \(AB=\sqrt5-1\), \(AC=\sqrt5+1\) and \(BC=x\). The area of triangle \(ABC\) is \(\frac{2\sqrt5}{3}\text{ cm}^2\). Angle \(A\) is acute.

(a) Find the exact value of \(\sin A\).

(b) Find the exact value of \(\cos A\) and hence find the exact value of \(x\).

(c) Find the exact value of \(\sin B\).