How can the circular function $\tan(\theta)$ be both a length and a ratio of lengths? The circular function  $\tan(\theta)$ is defined as $\tan (\theta)=\frac{\sin (\theta)}{\cos (\theta)}$. If we look at this in the context of the Unit Circle:

From this picture it can be seen that $\tan(\theta)$ is the $y$-coordinate of the $Q(1,y_1)$, the point on the terminal side of $\theta$ that lies on the vertical line $x=1$. So like $\sin(\theta)$ and $\cos(\theta)$ it signifies a length on the Unit Circle.
My question is: How can $\tan(\theta)$ be a length if it is a ratio of two lengths? The ratio of two lengths is dimensionless, so how does $\tan(\theta)$ signify a length?
EDIT: I guess this goes for $\sin(\theta)$ and $\cos(\theta)$ as well; as they are ratios of two lengths.
EDIT 2: mislabeled sine and cosine on the unit circle

$\sin \theta$ and $\cos\theta$ are themselves dimensionless (since they're ratios of length) but their value represent the magnitude of a length in the unit circle. 
