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I would like to calculate the change in length across a cuboid when looking at it from different angles (e.g. 10 and 20°).

In the illustration below the red arrows show the length I would like to calculate. Ideally, I would like to have an average of all the lengths across the cuboid. The aspect ratio between the width and length of the cuboid would be quite large (around 30).

Illustration cuboid at different angles



What equation would you suggest?

Please do not hesitate if there is anything unclear.

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  • $\begingroup$ (I added the image.) $\endgroup$ – Joseph O'Rourke Apr 25 at 23:32
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From the perspective of the cuboid, it looks like this:

enter image description here

When the cuboid is rotated by some angle $\theta$, $\cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$, so the rotated length will be equal to $\cos \theta$ multiplied by the width of the cuboid.

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    $\begingroup$ Hi Toby, thanks for your reply and the helpful drawing. Just to clarify. Wouldn't it actually be the cos 𝜃 = Adjacent / Hypotenuse in this case to calculate E->H in your drawing (what should correspond to the red arrows in my drawing)? $\endgroup$ – user3550552 Apr 26 at 22:01
  • $\begingroup$ Thanks for the correction. $\endgroup$ – Toby Mak Apr 27 at 1:55

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