Parallax, angle to observer etc.

[MathYew]

Hi,

I'm a mathematics analphabet, but still, sometimes I come across a problem, that I just can't keep away from. I hope someone finds this one worth a thought.
Here it is:
An observer is looking at a long object with marks spaced equally along its length (like a measuring rod or a check-board). The distance between the marks (or sizes of colored fields) is not given. So is not the distance from the observer. What is known, are all the angles between the marks from the observers standing point. My question is, is it possible to determine the angle of the "long object" in respect to the observers location given only the mentioned angles?

 

[DaveC426913]

It should be possible, yes.

A simple test is that you can easily identify the limits
- 90 degrees to line-of-sight. Angles at near and far end will be symmetrical.
- parallel to LoS: all angles are equivalent and equal to 0
so it should be possible to derive a unique answer for any angle in between.

 

[MathYew]

I think so, too. It seems obvious, there must be some intrinsic connection between these angles, but how to express it mathematicaly...? Some collegues of mine told me, it could be easily solved (with the law of cosinuses, I think) if one more parameter was given. Like the distance of the line of sight for example. But that's not the answer I'm looking for...

 

[zhentil]

As stated, it's false. Place the observer perpendicular to the measuring rod, and put only three hashes on it.

 

[DaveC426913]

As stated, it's false. Place the observer perpendicular to the measuring rod, and put only three hashes on it.

What do you mean?

If the observer sees three hashes, and the angles formed by the outermost two hashes are equivalent, the observer knows conclusively that the measuring stick is perpendicular to his line of site.

QED.


BTW, who said there is a limit on the number of hash marks? Seems to me, if not stated, we have our choice. (Not that it matters. Three is all you'll need.)

 

[MathYew]

Ok, here's the original form of this problem. Maybe it will make it more interesting. =)

A submarine sonar man hears a ship propeller noise at a certain angle from the still submarine (AOB - angle on bow). He makes timed observations of the AOB. Considering that the RPM of the propeller is constant, he can assume the distance traveled by the ship in equal time to be equal, but he can not tell the exact distance from the submarine, nor can he determine it's speed. Can he determine it's course?
In reality, I'm certain, he can get much more data than this, but still... :) Maybe his instruments have been depth-charged. :D