To find the length of side \( AC \) in triangle \( \triangle ABC \) using the sine ratio, we start by noting the relevant angles and sides. Given that \( \angle A = 90^\circ \) and \( \angle B = 25^\circ \), \( \angle C \) can be found since the angles in a triangle sum to \( 180^\circ \). Thus, \( \angle C = 180^\circ - \angle A - \angle B = 180^\circ - 90^\circ - 25^\circ = 65^\circ \).
The sine ratio states that:
\[ \sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}} \]
For angle \( B \):
\[ \sin(B) = \sin(25^\circ) = \frac{AC}{BC} \]
Where \( AC \) is the side opposite angle \( B \) and \( BC \) is the hypotenuse. Given that \( BC = 5 \) inches, we can rearrange the formula:
\[ AC = BC \cdot \sin(25^\circ) \]
Substituting \( BC = 5 \):
\[ AC = 5 \cdot \sin(25^\circ) \]
Thus, out of the provided options:
- AC = 5 sin(25°)
is the correct response.
The other options, including those with sine of 65 degrees or fractions, do not apply for finding side AC opposite angle B in this context. Therefore, the correct answer is:
AC = 5 sin(25°).