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Mathematical problem

Community Veteran
Posts: 16,820
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Registered: 06-11-2007

Mathematical problem

I know there are some mathematical genii (geniuses/geni`s) (whatever) out there, and I have a problem I would like answered....
If an object "appears" to be .5 of an inch (in size) when the known size is 48 inches,
what is the formula for working out how far away that object is? and what is the answer, please..
I suspect it is to do with geometry, and triangles, but it is so long since I did any stuff like that I have forgotten it all.... !  Roll eyes
(and I am getting older every day)  Cheesy
27 REPLIES
Community Veteran
Posts: 1,100
Registered: 05-04-2007

Re: Mathematical problem

I thought that is what Laser Range Finders were invented for  Wink Grin
Community Veteran
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Re: Mathematical problem

Wrong answer Undecided
geewizz
Grafter
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Re: Mathematical problem

You need to know the distance from the eye to the virtual mesuring point too.
Community Veteran
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Registered: 06-11-2007

Re: Mathematical problem

Hmm!  Perhaps that will be the problem..... I wanted to be able to work out the distance, knowing the other measurement....  Undecided Cry
geewizz
Grafter
Posts: 1,125
Registered: 01-08-2007

Re: Mathematical problem

Knowing what other measurement?
Split the problem into triangles. You know the size of the base of the big triangle and the size of the base of the small triangle. All other variables are unknowns. Unless you can provide at least one other variable (length or angle) then you don't have enough information to make any calculations about the proportional relationships.
If you vary the distance of the virtual measurement point from the eye then that 0.5" measurement changes so you can't make any headway without knowing how far it is from the eye OR how far it is from the object.
And if you really wanted to get accurate results then you would need to know the angle of the ground, the  height of the eye from the ground, the angle you are holding the mesuring plane and any difference between that angle and the angle of the distant object etc.
Community Veteran
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Re: Mathematical problem

Yea!  Thanks for the explanation and the diagram.... I only know the size of the object, and the "approximate" size that it appears to be, at the distance `X` from me..... unfortunately, the other variables, (the angles) are unknown also, so it looks like the end of the problem.... Cry
Thanks again... Wink
Community Veteran
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Re: Mathematical problem

Just had a thought... ! 
At arms length, my thumbnail is 28 inches from my eye, and is half an inch, the angle between the base of the nail, and the top of the nail is 5 degrees....
Now, is it possible to advance those two lines to an assumed 48 inches for the actual object size, then calculate the distance from the eye to the object?
Or am I going off on a tangent ? ? ? ?

geewizz
Grafter
Posts: 1,125
Registered: 01-08-2007

Re: Mathematical problem

Quote from: The
You need to know the distance from the eye to the virtual mesuring point too.

Quote from: shutter
At arms length, my thumbnail is 28 inches from my eye,

That's the variable you failed to recognise before. You have all the measurements you need to calculate (roughly) the distance to your object.
We'll assume that the thumbnail and the object are on the same plane and we will just ignore ground level and elevation, just to keep things simple. So now we will consider the problem in the form of an issoceles triangle where the eye is at the angle opposite the base, and that base will be the height of the distant object.
We can now dissect the triangle with a line parallel to the base. This represents the thumbnail. The distance between your eye and the thumbnail will be represented by the side of the smaller triangle.
Lets call the bases B1 and B2
& we'll call the sides S1 and S2
B2/B1 = S2/S1
48/0.5 = S2/28
96 = S2/28
S2 = 28*96
S2 = 2688" or 224'
Community Veteran
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Re: Mathematical problem

Right ! ...   Smiley    Got it !..    Smiley   
. Now I can use the formula (and my thumbnail) when out and about, to give me the distance....
Thank you for the lesson..... much appreciated. Wink

EDIT EDIT EDIT
Check out my blog, to see why I wanted to know how to do this ! ! !.... Smiley

http://nemosphotography.blogspot.com/
Community Veteran
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Registered: 02-10-2008

Re: Mathematical problem

Just as well you never did the Navigation then Shutter  Wink Smiley
Astro nav was a real pain - but I never had to do it practise - even trying to help colleagues with their "homework" was bad enough
Community Veteran
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Re: Mathematical problem

Actually, I did do some navigation, from Portsmouth to Alderney, C.I. on an M.F.V.  which involved working out the tides, direction and changes, and securing the boat in the harbour .... it was not until we had safely moored up, that I read the Pilot Notes, on Alderney, which said " Entering Alderney harbour at night should not be attempted, without a pilot, or good local knowledge " ! ! !...we entered just after sunset, (it was dark), and moored up between the first & second buoys, without any problems !  Smiley
But way back then, we had just finished Nav school, and it was all "fresh"....
Not sure if I could do it now 40 years on ! Undecided
Community Veteran
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Registered: 02-10-2008

Re: Mathematical problem

By chance - that is where I once almost came to grieve in a RN yacht - we set out from Guernsey, and come nightfall I was duty cox and all others were below.
I followed the course I was given ( honest ) and after an hour or so I spotted something ahead in the moonlite sea - and the noise level rose.
I got the navigotor up on deck, and showed him - he quickly told me to go about and head off at an angle of 90.
We had almost run onto the Casquets - a  line of rocks just below or on the surface. It was the white foam as they water hit the rocks that I saw and heard.
I was vindicated - the nav had miscalculated the tidal flow !!!. 
http://en.wikipedia.org/wiki/Casquets
Community Veteran
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Re: Mathematical problem

Yes, many a ship has foundered thereabouts!...  Shocked  the Minques, also come to mind in that area too !...  Shocked
Community Veteran
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Re: Mathematical problem

The answer is simple take the error due to parallax + the cohesion of linear expansion  * sq of any prime number /the day of the week and then see if these links do what you are after
http://www.1728.com/angsize.htm
http://www.canon.com/bctv/calculator/calculator3.html
http://www.cfa.harvard.edu/webscope/activities/pdfs/measureSize.PDF