Given a right triangle with sides $a$, $b$, and hypotenuse $c$, and angle $\theta$ opposite side $a$, which of the following correctly expresses $\sin \theta$ in terms of the triangle's sides?

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

Answer: (B)

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 angle \(\theta\).
3. Identify the hypotenuse of the triangle, which is the longest side and is given as \(c\).
4. Substitute these sides into the sine definition: \(\sin(\theta) = \frac{a}{c}\).
5. Therefore, the correct expression for \(\sin(\theta)\) in terms of the triangle's sides is \(\sin(\theta) = \frac{a}{c}\).