Intuition around why Sine of X angle always equals same result. My understanding so far. 
Sine represents a ratio of two sides of an interior angle within a right angle triangle. So given the three lengths of a triangle you can find the sine of any of the 3 interior angles. 
Also if you are given the actual angle of an interior angle, you can get the sine using a calculator.
Thus, I deduce from these two statements that on a right triangle any interior angle of a specific number represents a constant raio, whatever the area of the triangle.
I can visualize that in my head to a certain extent, scaling the triangles sides equally, increases the area of the triangle but not the ratio of the sides.
But I'm wondering if I'm missing anything in terms of intuition around this?  
 A: I think Michael Hardy has rephrased the question well, and I think The Chaz has answered it by referring to similar triangles. If two right triangles both have an angle $\theta$, then they are similar, so the ratio opposite-to-hypotenuse will be the same in both, so the sine depends only on the angle and not on the area. 
A: What is at stake here is that in euclidean geometry thanks to the parallel axiom we have the notion of similarity: We can scale our figures by an arbitrary factor $\lambda>0$, whereby all incidences stay intact, all lengths are multiplied by $\lambda$, and all angles stay the same. This additional transformation group is not present in other geometries (which apart from the parallel axiom satisfy much the same axioms): You cannot enlarge a spherical triangle "linearly" by a factor $\lambda>0$ whereby all angles stay the same.
A: "For example what happens in non-90 degree triangles with sine?"  There are a ton of interesting trig equalities that apply to any triangle, such as the fact that the ratio of each side to the angle opposite is the same for all 3 angles/sides - the Law of Sines.  You should totally read "Trigonometry" by Gelfand and Saul - hugely informative and fun to read.
