How frustrating, I think when I was 11 years old I could have done this in approximately 30 seconds, now more than a quarter of a century later my brute force methods lead me to a horrific looking equation that can't be optimal!. Please check attached image, this is the projection of an image at one distance (100cm) viewed at another distance (160cm), I need to find out the "measured" size either side of the centre of the projection based on a presumed "tilt" at the second measuring surface. I am sure there is some kind of triangle based wizardry that makes this a simple matter to express the (unequal) two distances as a ratio to their (equal) values in an untilted world. Thanks for any help
well, playing with adding angles of triangles up, am i right in thinking that the angles are
90 - tilt angle (BXT) + divergence angle (the half angle at the very top triangle)
and
90 + tilt angle - divergence angle
but I suppose the divergence angle will vary based on the width of the triangles at the depths 100 and 160cm
ohhhhhhh..............
It is possible to derive a formula for the required ratio based on that angle, but it is MUCH easier if you know something else as well. For example, do you know the measure of angle FAD?
Also, will AD and AX always be the 100 and 160 respectively, or should these distances be treated as variables?
Ok, I've worked on this for a fair bit now - I like puzzles. But I can't figure it out without knowing something else besides the lengths of AD and AX. Maybe you shouldn't be quite so frustrated!
In general it is true - you've got to know three things about a triangle to know everything about it. The problem here is that the vertex angle (at A) also effects the ratio between Gx and CX.
I am beginning to believe I was wrong in my previous post about the possibilities of deriving a formula for you. But again, it would be a fairly easy proposition if you know one more thing about this situation.
Yeah, I just mean the angle DAE is the inverse tan of 1/20, in the case that DE = 5cm (a common real example of what it might measure in my situation), of course you don't need to include the fact that XB = 8cm, this just shows tan-1 of DAE is 8/160 rather than 5/100, i.e. the same thing. Of course specifying DE = 5cm is not a generic example!