How to find length when viewing at some angle?

Question

I have a question on angles. I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some angle. Below I have attached an image for more clarity. So how do I find y in the image below?

Answer 1

If $ \ \theta \ $ is the angle that the line-of-sight makes to the surface of the tile, then $ \ x \ $ can be treated as the hypotenuse of a right triangle for which $ \ y \ $ is the length of the leg opposite $ \ \theta \ $. Thus, $ \ y \ = \ x \ \cdot \ \sin \theta \ .$

This can be checked easily: if the line-of-sight is face-on to the tile, $ \theta \ = \ 90^{\circ} \ $, so $ y \ = \ x \cdot 1 \ = \ x \ ;$ if the line-of-sight is along the surface, $\theta \ = \ 0^{\circ} $ and $y \ = \ x \cdot 0 \ = \ 0 \ .$ Other angles will produce intermediate values for $y$ .

Answer 2

Your pictures are misleading. If you look at the rectangular in image A from an angle it will not look like the image in B. Make the shape in image B into a 3D image, you'll see it is misleading