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