In right triangle $JKM$, if angle $K$ is the right angle, which of the following correctly expresses $sinJ$ in terms of the side lengths?

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

Answer: (A)

Verified step by step guidance

1. Identify the right angle in triangle JK M, which is angle K. This means side JM is the hypotenuse, as it is opposite the right angle.
2. Recall the definition of sine for an angle in a right triangle: \(\sin(\theta) = \frac{\text{length of side opposite to } \theta}{\text{length of hypotenuse}}\).
3. Determine which side is opposite angle J. Since angle K is right, the side opposite angle J is side KM.
4. Identify the hypotenuse, which is side JM, the side opposite the right angle K.
5. Express \(\sin(J)\) as the ratio of the length of the side opposite angle J to the hypotenuse: \(\sin(J) = \frac{KM}{JM}\).