I am asked find the following limit
$$\lim_{\theta \rightarrow 0}\frac {\sin^2\theta}{\theta}$$
I recognize that $$\lim_{\theta \rightarrow 0}\frac{\sin\theta}{\theta}=1$$
But because I have $sin^2\theta$ in the numerator, I am left with...
$$\lim_{\theta \rightarrow 0}1(\sin\theta)$$
When I think about what this implies, I reason that the ratio of the opposite side over hypotenuse of the angle $\theta$ must approach approach zero, but for this to happen the opposite side would have a value of zero, which means the triangle formed would have no x component.
$$\lim_{\theta \rightarrow 0}1(\sin\theta)=0$$
Is my reasoning correct? Am I thinking about this question in a constructive manner?