[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\\\\
-------------------------------\\\\
\begin{array}{rllll}
(-6&,&5)\\
\uparrow &&\uparrow \\
a&&b\\
x&&y
\end{array}\impliedby \textit{let's find the \underline{hypotenuse}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{(-6)^2+(5)^2}\implies c=\sqrt{36+25}\implies \boxed{c=\sqrt{61}}
\\\\\\
sin(\theta)=\cfrac{5}{\sqrt{61}}[/tex]
now, let's rationalize the denominator
[tex]\bf \cfrac{5}{\sqrt{61}}\cdot \cfrac{\sqrt{61}}{\sqrt{61}}\implies \cfrac{5\sqrt{61}}{(\sqrt{61})^2}\implies \boxed{\cfrac{5\sqrt{61}}{61}}[/tex]
