To find the value of \(\sin \theta\) given the sides \(c\) and \(b\), we can use the definition of sine in the context of a right triangle.
In a right triangle, where \(c\) is the length of the hypotenuse and \(b\) is the length of one of the legs (adjacent or opposite to \(\theta\)), we have:
\[ \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}. \]
From your problem, we might interpret \(b\) as the length of the opposite side and \(c\) as the hypotenuse. Therefore,
\[ \sin \theta = \frac{b}{c} = \frac{15}{17}. \]
So the value of \(\sin \theta\) is:
\[ \frac{15}{17}. \]
Since you mentioned that no simplification is required, the value remains as:
\[ \frac{15}{17}. \]
This fraction represents \(\sin \theta\) based on the given dimensions.