Given a right triangle $△abc$, which of the following triangles represents the image after applying the sine function to angle $A$ to find the ratio of the length of the side opposite angle $A$ to the hypotenuse?

• A. Triangle 4, where the ratio is $\frac{\mathrm{AB}}{\mathrm{AC}}$
• B. Triangle 1, where the ratio is $\frac{\mathrm{BC}}{\mathrm{AC}}$
• C. Triangle 3, where the ratio is $\frac{\mathrm{AC}}{\mathrm{AB}}$
• D. Triangle 2, where the ratio is $\frac{\mathrm{AB}}{\mathrm{BC}}$

Answer: (B)

Verified step by step guidance

1. Recall the definition of the sine function in a right triangle: for an angle \( A \), \( \sin(A) = \frac{\text{opposite side}}{\text{hypotenuse}} \).
2. Identify the sides relative to angle \( A \) in triangle \( \triangle ABC \): the side opposite \( A \) is the side that does not touch \( A \) except at a vertex, and the hypotenuse is the longest side opposite the right angle.
3. Determine which side is the hypotenuse by locating the side opposite the right angle in the triangle. This side will be the denominator in the sine ratio.
4. Find the side opposite angle \( A \) to use as the numerator in the sine ratio.
5. Compare the given ratios in the options to the correct sine ratio \( \sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} \) and select the triangle whose ratio matches this definition.