The whole point of trig is the ratios of the sides of right triangles. As long as the triangles are proportional, the ratios will always be the same.

The two triangles above are similar. That means that the larger one is the same exact shape, but each side is twice as large.

{\renewcommand{\arraystretch}{2}

\begin{tabular}{c | c}

Small triangle & Big triangle\\ \hline

& \\

& \\

&

\end{tabular}} \quad

Since the lengths of the sides are proportional (multiplied by 2), the trig ratios are the same. \\

{\renewcommand{\arraystretch}{2}

\begin{tabular}{c | c}

Small triangle & Big triangle\\ \hline

& \\

& \\

&

\end{tabular}} \quad