Intuition behind $\sin(\theta)$ when introducing this to high school students When first introducing trigonometry to students, the traditional setup is to start with a right-angled triangle with reference angle $\theta$ and we label the sides with "Hypotenuse, Opposite and Adjacent."
To keep students engaged with some practicality behind this, we can give an example of trying to figure out the height of a tree, know how far you are from the base of the tree and estimating the angle to the top of the tree.
Then we define something arbitrary called "$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$".
I feel like at this point, students lose the conceptual intuition behind what's going on. Some students who are able to just accept it without questioning it too much can start punching in numbers and angles into the calculator when doing example questions. Other students who feel stuck with this weird idea might not be able to move forward.
What would be a good idea to explain how to think about $\sin(\theta) $? I don't want to introduce a unit circle type definition because I feel like it will only make it less tangible for them. Can we do better than something like "it's a magic computer which tells you the ratio of the opposite and hypotenuse sides of a right-angled triangle when you supply it the reference angle"
To maybe elaborate/clarify: I feel like a few things that students might not be able to understand
If you take the tree example from above, we have the adjacent side and the angle. Now:

The definition of $\tan(\theta)$ is the missing quantity we wanted in
  the first place. The ratio of the opposite side and the adjacent side.
  But how does $\tan$ go and calculate the ratio when I give it a
  angle?

I think it's possible to convince them - once I have this ratio, I can find the length of the missing side: $\text{Opposite} = \tan(\theta)\times \text{Adjacent}$.

You can sell sine and cosine based on expressing how much of the right triangle in question aligns with the adjacent or opposite side. 
Let us set notation,


*

*$A$ = adjacent side length

*$B$ =  opposite side length

*$C$ = hypotenuse side length


Since the triangle is assumed to be a right triangle we know $A^2+B^2=C^2$. Let $\theta$ be the angle between $A$ and $C$.


*

*the hypotenuse is the longest side; $A,B \leq C$

*the only way for $A=C$ is that $\theta = 0^o$ (this happens when $B=0$

*if we imagine $A$ shrinking to zero we see $\theta$ gets close to $90^o$
We can introduce sine and cosine as devices to express how much of $C$ is used in forging $A$ or $B$:


*

*$A = C \cos \theta$

*$B = C \sin \theta$
Notice since $A,B \leq C$ we must have $\cos \theta, \sin \theta  \leq 1$. Also, when $\theta = 0$ we noted $A=C$ hence $\cos 0 = 1$ whereas $\sin 0 = 0$. Conversely, from the case of $A \rightarrow 0$ we saw $B=C$ and $\theta = 90^o$ hence $\cos 90^o = 0$ whereas $\sin 90^o = 1$.
Of course, there are much better ways. But perhaps this is sort of in the direction you seek ?
