In a right triangle, if $a$ and $c$ are the lengths of the leg and hypotenuse respectively, which of the following expressions represents $sin\theta$ where $\theta$ is the angle opposite side $a$?

• A. $\frac{b}{c}$
• B. $\frac{c}{b}$
• C. $\frac{a}{c}$
• D. $\frac{c}{a}$

Answer: (C)

Verified step by step guidance

1. Recall the definition of sine in a right triangle: \(\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}\).
2. Identify the side opposite to angle \(\theta\). According to the problem, side \(a\) is opposite to \(\theta\).
3. Identify the hypotenuse of the triangle, which is the longest side, given as \(c\).
4. Substitute these values into the sine definition: \(\sin(\theta) = \frac{a}{c}\).
5. Compare this expression with the given options to confirm that \(\frac{a}{c}\) correctly represents \(\sin(\theta)\).