In triangle ABC, where angle A is the right angle, angle B is 25 degrees, and side BC is the opposite side to angle B, we can determine the length of side AC using the sine ratio.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case:
- \( \text{Opposite side (BC)} = 5 \text{ inches} \)
- \( \text{Hypotenuse (AC)} \)
Using the sine ratio for angle B:
\[ \sin(B) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AC} \]
Substituting the values:
\[ \sin(25^\circ) = \frac{5}{AC} \]
To find AC, we can rearrange this equation:
\[ AC = \frac{5}{\sin(25^\circ)} \]
Thus, the correct option that uses the sine ratio to find the length of AC is:
\[ AC = \frac{5}{\sin(25^\circ)} \]
So, the correct choice is:
ac = 5/sin 25 degrees.
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