Length of a Side

Level pending

In triangle \(ABC\), \(\angle B=30^{\circ}\), \(\angle C=90^{\circ}\), and \(D\) is a point on side \(BC\) such that \(\overline{BD}=56\) and \(\angle ADC=45^{\circ}.\) The length of side \(AC\) can be expressed as \(p\sqrt{3}+p.\) What is the value of \(p?\)

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