In a right triangle, if the acute angles are \(\theta\) and \(\phi\), we have the relationship:
\[ \theta + \phi = 90^\circ \]
This means that \(\phi = 90^\circ - \theta\).
By using the sine and cosine complementary angle identity, we find that:
\[ \sin \phi = \cos \theta \]
Given that \(\sin \phi = 0.25\), we can then conclude:
\[ \cos \theta = 0.25 \]
Thus, the value of \(\cos \theta\) is 0.25.
So, the answer is:
0.25