In right triangle $\Delta ABC$, assume the right angle is at $C$. Which expression is equivalent to $\sin \left(A\right)$?

• A. $\frac{BC}{AC}$
• B. $\frac{BC}{AB}$
• C. $\frac{AB}{BC}$
• D. $\frac{AC}{AB}$

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle \( \triangle ABC \) with the right angle at \( C \). The side opposite the right angle \( C \) is the hypotenuse, which is \( AB \).
2. Recall the definition of sine for an angle in a right triangle: \( \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \).
3. For angle \( A \), determine which side is opposite to it. Since the right angle is at \( C \), the side opposite angle \( A \) is \( BC \).
4. Identify the hypotenuse of the triangle, which is the side opposite the right angle \( C \), so the hypotenuse is \( AB \).
5. Write the expression for \( \sin(A) \) using the opposite side and hypotenuse: \( \sin(A) = \frac{BC}{AB} \).