To find the value of \(\sin \theta\) given \(c = 17 \text{ in.}\) and \(b = 15 \text{ in.}\), we can use the sine rule or the relationship in a right triangle depending on the context.
Assuming this is a right triangle, where \(c\) is the hypotenuse and \(b\) is one of the sides, then:
\[ \sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{b}{c} \]
Here, we have:
\[ \sin \theta = \frac{15 \text{ in.}}{17 \text{ in.}} \]
Therefore, the value of \(\sin \theta\) is:
\[ \sin \theta = \frac{15}{17} \]
This fraction does not require simplification.
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