If you rise the eye up, then the pole obscure LESS of the object.
But rise up from what height? That's the part you didn't include in the what was known or fixed. When I mentioned it in my first post you asked why it mattered, so that's what everything's been about since: why does it matter how high the observer's eye is when 3' behind the pole. I'm trying to explain to you that different heights will provide different angles for the hypotenuse (the line connecting the top of the pole with the top of the object), and thus different ratios.
Yeah, and since then I have attempted to write exactly why you are wrong but:
A) You are incapable of understanding it; or,
II) You do understand why your point is meaningless and bears not on the issue at hand and are being purposefully obtuse.
The only way for one to accurately measure for an unknown height of a distant object where the base line distance to the base of the object is known is to place a pole in between the line of sight of the TOP of the object and have that pole cover the remainder of the object.
That means placing your eye level with the base of the pole. And to get the tops to line up your eye is 3' behind the pole, then your ratios work.
But it's not the only way. You can stand and work in your height. And to keep the ratios the same in the same scenario, you'll be closer than 3' behind the pole.
But you didn't specify whether eye level was at toe level or standing eye level. It matters. If you're 3' behind the pole and your eye is 5' high when aligning the pole's top with the distant object, the angle will be shallower and your calculation of ratios different.
You can't be just at any height if a fixed 3' behind the pole and use the ratios you cited. They only work from one elevation 3' behind the 10' pole, and that's with your eye at ground level.
If that's what you were trying to depict in the first place. Fine. And I said if true, no problem. But you asked why it matters, and that's what I've been telling you. It matters to the triangle/ratio whether your standing or lying on the ground, given the "KNOW, FIXED and OBSERVED" figures you provided.
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No, it does not.
If one were to stand further away, of course the fixed values would remain the same.
The variable in the measurement will always remain
x.
The other numbers (the height of pole, distance to object from the observer as measured along the base, distance from pole to observer) can have any value. That would determine the angle of the hypotenuse.
But the angle of the hypotenuse is not necessary to make the calculation.
You know that so everything you have written here has been purposeless.