Answer
$\dfrac{7\sqrt{53}}{53}$
Work Step by Step
First determine $x,y$ and $r$:
$(x,y)=(2,7)$
$x=2$
$y=7$
Solve for $r$ using the formula $r^2=x^2+y^2$:
$r^2=x^2+y^2\\
r^2=2^2+7^2\\
r^2=53$
$r=\pm\sqrt{53}$
Since $r$ is never negative, then $r=\sqrt{53}$.
Compute $\sin\theta$:
$\sin\theta=\dfrac{y}{r}=\dfrac{7}{\sqrt{53}}=\dfrac{7\cdot \sqrt{53}}{\sqrt{53} \cdot \sqrt{53}}=\dfrac{7\sqrt{53}}{53}$
