In the right triangle \( \triangle ABC \), where \( \angle A = 90^\circ \), \( \angle B = 25^\circ \), and \( \angle C = 65^\circ \), we are tasked with finding the length of \( AC \) using the sine ratio.
Since \( BC \) is the side opposite \( \angle A \) and \( AC \) is the side adjacent to \( \angle B \), we can use the sine ratio associated with \( \angle B \):
\[ \sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{BC} \]
Here, \( BC \) is the hypotenuse (which is given as 5 inches) and \( AC \) is the opposite side to \( \angle B \).
Thus, we have:
\[ \sin(25^\circ) = \frac{AC}{5} \]
Rearranging this gives:
\[ AC = 5 \cdot \sin(25^\circ) \]
So, the correct response using the sine ratio to find the length of \( AC \) is:
AC = 5sin25°.
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