Question

right triangle jkl is shown. which trigonometric values are equal to \\(\frac{8}{17}\\)? \\(\circ\\) \\(\sin(k)\\) \\(\circ\\) \\(\sin(j)\\) \\(\circ\\) \\(\cos(k)\\) \\(\circ\\) \\(\cos(j)\\) \\(\circ\\) \\(\tan(k)\\) \\(\circ\\) \\(\tan(l)\\)

Explanation:

Step1: Recall trigonometric ratios

For right triangles:
$\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Analyze $\sin(J)$

Opposite side to $\angle J$ is $8$, hypotenuse is $17$.
$\sin(J)=\frac{8}{17}$

Step3: Analyze $\cos(K)$

Adjacent side to $\angle K$ is $8$, hypotenuse is $17$.
$\cos(K)=\frac{8}{17}$

Step4: Verify other options

$\sin(K)=\frac{15}{17}$, $\cos(J)=\frac{15}{17}$, $\tan(K)=\frac{15}{8}$, $\tan(L)$ is undefined (right angle). These do not equal $\frac{8}{17}$.

Answer:

$\sin(J)$, $\cos(K)$