Given a right triangle with angle $LJK$ at vertex $J$, which equation can be used to find the measure of angle $LJK$ if the length of the side opposite $LJK$ is $a$ and the hypotenuse is $c$?

• A. $\cos \left(LJK\right)=\frac{a}{c}$
• B. $\sin \left(LJK\right)=\frac{a}{c}$
• C. $\cos \left(LJK\right)=\frac{c}{a}$
• D. $\sin \left(LJK\right)=\frac{c}{a}$

Answer: (B)

Verified step by step guidance

1. Identify the sides relative to angle \(LJK\): the side opposite the angle is given as \(a\), and the hypotenuse is \(c\).
2. Recall the definition of the sine function in a right triangle: \(\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}\).
3. Apply this definition to angle \(LJK\), so \(\sin(LJK) = \frac{a}{c}\).
4. Check the other trigonometric ratios to confirm which matches the given sides: cosine is adjacent over hypotenuse, which does not fit \(\frac{a}{c}\) since \(a\) is opposite, not adjacent.
5. Conclude that the correct equation to find the measure of angle \(LJK\) is \(\sin(LJK) = \frac{a}{c}\).