Given right triangle JKL, where angle $K$ is the right angle, if $\mathrm{JK}$ = $5$, $\mathrm{KL}$ = $12$, and $\mathrm{LJ}$ = $13$, what is the value of $sinJ$?

• A. $\frac{12}{13}$
• B. $\frac{5}{13}$
• C. $\frac{13}{12}$
• D. $\frac{5}{12}$

Answer: (A)

Verified step by step guidance

1. Identify the right angle in triangle JKL, which is angle K. This means sides JK and KL are the legs, and LJ is the hypotenuse.
2. Recall that the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).
3. Determine which side is opposite angle J. Since angle K is the right angle, the side opposite angle J is KL.
4. Use the given side lengths: opposite side to angle J is \$12\( (KL), and the hypotenuse is \)13$ (LJ).
5. Write the sine of angle J as \(\sin(J) = \frac{12}{13}\).