In triangle \( \triangle ABC \), where \( \angle A = 90^\circ \), \( \angle B = 25^\circ \), and \( BC = 5 \) inches, we are interested in finding the length of \( AC \).
To determine the correct use of the sine ratio, we need to recall that in a right triangle, the sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse.
Since \( \angle B = 25^\circ \), the length \( AC \) is opposite to \( \angle B \), and \( BC \) is the hypotenuse. Thus, we can use the sine of angle \( B \):
\[ \sin(B) = \frac{\text{opposite (AC)}}{\text{hypotenuse (BC)}} \]
This gives us:
\[ \sin(25^\circ) = \frac{AC}{5} \]
We can rearrange this to find \( AC \):
\[ AC = 5 \sin(25^\circ) \]
Therefore, the option that correctly uses the sine ratio to find the length of \( AC \) is:
AC = 5 sin(25°)