По основному тригонометрическому тождеству:
\({\sin ^2}A + {\cos ^2}A = 1\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\sin A = \sqrt {1 — \frac{1}{{17}}} = \frac{4}{{\sqrt {17} }}\).
Тогда: \({\rm{tg}}\,A = \frac{{\sin A}}{{\cos A}} = \frac{4}{{\sqrt {17} }}:\frac{{\sqrt {17} }}{{17}} = \frac{4}{{\sqrt {17} }} \cdot \frac{{17}}{{\sqrt {17} }} = 4\).
По определению тангенса из треугольника ABC:
\({\rm{tg}}\,A = \frac{{BC}}{{AC}}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,4 = \frac{2}{{AC}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,AC = 0,5\).
Ответ: 0,5.