Question 103·Medium·Geometry and Trigonometry

Use the Pythagorean theorem with the two labeled legs to find the length of $JL$.

For angle $J$, $\sin\theta$ is the length of the side opposite angle $J$ divided by the hypotenuse.

In Desmos, enter sqrt(8^2+15^2) to compute $JL$.

Use the opposite side from the diagram ($15$) and divide by the hypotenuse value you computed. Enter 15/17 to get the exact ratio.

Angle $J$ is $\theta$. The side opposite angle $J$ is $KL$, and the hypotenuse is $JL$ (the side across from the right angle at $K$).

The legs are $JK=8$ and $KL=15$, so

So the correct choice is $\dfrac{15}{17}$.