In triangle \( ABC \) with \( \angle A = 90^\circ \) and \( \angle B = 25^\circ \), we can find the length of side \( AC \) using the sine ratio. The sine ratio states that:
\[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \( \angle B = 25^\circ \). The side opposite \( \angle B \) is \( AC \), and the hypotenuse \( BC \) is given as 5 inches.
From the sine definition for angle \( B \):
\[ \sin(25^\circ) = \frac{AC}{BC} \]
Substituting the hypotenuse:
\[ \sin(25^\circ) = \frac{AC}{5} \]
To solve for \( AC \):
\[ AC = 5 \sin(25^\circ) \]
Thus, the corresponding choices you provided would be:
- AC = 5 sin 25° \[ upper A upper C equals 5 sine 25 degrees \]
This option is correct and uses the sine ratio appropriately to find the length of \( AC \).