To find the length of \( AC \) in triangle \( ABC \) using the sine ratio, we will use the angle opposite to the side we are looking for. In this case, we have:
- \( \angle A = 90^\circ \)
- \( \angle B = 25^\circ \)
- \( \angle C = 65^\circ \) (since the angles in a triangle sum to 180°, \( 180^\circ - 90^\circ - 25^\circ = 65^\circ \))
Since we are interested in finding the length of \( AC \), we can use the sine of angle \( B \) (which is opposite \( AC \)):
The sine ratio is defined as:
\[ \sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{BC} \]
Rearranging gives:
\[ AC = BC \cdot \sin(B) \]
Substituting the known values:
- \( BC = 5 \) inches
- \( B = 25^\circ \)
Thus,
\[ AC = 5 \cdot \sin(25^\circ) \]
Therefore, the correct option that uses the sine ratio to find the length of \( AC \) is:
\[ AC = 5 \sin(25^\circ) \]
So the correct response is:
AC = 5 sin 25°
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