I have two images:
Both are views of the same object. The first depicts the 2D coordinates (relative to your browser for instance); the second depicts the 3D coordinates.
My question is, is there some magic number such that the height of the wall can be an integer in both pictures? (I am very doubtful.)
Note that the number 58.786 in the first image is equal to 48 * cos(30°) * sin(45°) * 2. The wall height in the second image is 48.
Thanks.
No, because $\cos(30^o)\sin(45^o)$ is irrational. However, $$\frac{58.786}{96} \approx \frac{30}{49} \approx \frac{49}{80} \approx \frac{79}{129}$$
You probably should know that human perception of height does not match human perception of width. A few percent difference or error in the height is not perceptible to us humans at all. (That is, an ellipse will look absolutely circular to us humans, even if its width and height differ by a few percent. Similarly for squares and other shapes.)
In fact, in something like computer graphics, you can use 2:3 here, or any multiples like 64:96, and nobody will perceive any error.