Which of the following is the correct definition of the sine function for an acute angle $\theta$ in a right triangle?

• A. $\frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}$
• B. $\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}$
• C. $\frac{\mathrm{opposite}}{\mathrm{adjacent}}$
• D.

Answer: (B)

Verified step by step guidance

1. Recall that in a right triangle, the sine of an acute angle \( \theta \) is defined as the ratio of the length of the side opposite to \( \theta \) to the length of the hypotenuse.
2. Identify the three sides relative to the angle \( \theta \): the opposite side (across from \( \theta \)), the adjacent side (next to \( \theta \)), and the hypotenuse (the longest side opposite the right angle).
3. Write the sine function as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
4. Compare this definition with the given options to determine which fraction matches the sine function's definition.
5. Conclude that the correct definition of sine for an acute angle \( \theta \) in a right triangle is \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).