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Calcing length of object using trig

  1. Nov 8, 2006 #1


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    I've been asked by a friend edting a textbook to find the exact dimensions of the Freedom Arches at Nathan Phillips Square. (N43 39'08.23" W79 22'59.63").

    I've looked everywhere online and haven't found it. But I'm trying to estimate it from a Google map.

    Google Earth shows them to be 300 pixels long at a distance of 456ft. I should be able to calculate that dimension in feet using trig - but for the life of me, I can't figure out how.

    I realise that, if I can fond an object of known length on thje map, I'm home free, but that's fraught with pitfalls and is not the only way I should be able to do it.

    If I'm trying to calc the height of a triangle, and I know the base length, all I need is the angle. How do I figure out the angle here?
    Last edited: Jul 20, 2007
  2. jcsd
  3. Nov 8, 2006 #2
    Linear feet?

    tan(angle) = height/base
    Last edited: Nov 8, 2006
  4. Nov 9, 2006 #3


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    Well, you know what I mean.

    n'K, I know the formula.

    Height is the result I want (thus is an unknown).
    But I can't figure out how I'd know the angle.
  5. Nov 9, 2006 #4
    Am I missing something?...you should be able to calculate the length using the Ruler, although it shows only the length between the ends of the arches and not the actual (arc)length. But you may be able to calculate the lenght of arch itself once you know the base length and equation of the arc(h). :biggrin:
  6. Nov 9, 2006 #5


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    No, I'm missing something. That's why I'm asking.

    All I'm trying to figure out is, if I'm 456ft away from it, and I want to know how long it is in feet...

    No, the more I think about it, the more I realize it can't be done. I don't have enough information.

    I can't calc the angle. The angle is determined by the focal length of the lens, which I don't know (think about it: at a given altitude of 456ft, a fisheye lens should show the arches at a very different angular size than a telephoto. I'd have no way to determine that angle without knowing that).

    The only way I can do this is to find a known quantity on the map, and measure its length in pixels, then compare that to the arches.

    And it has to be something very nearby, or I can't trust the numbers (changes in altitude, mapping session, etc)

    The Skydome has units I can locate, and it is in the same frame and at the same altitude.

    My calcs put the arches at 114ft long. (This jives with another stat I read somewhere, saying that the pool is approx. (approx!) 100x200ft.)
    Last edited: Nov 9, 2006
  7. Nov 9, 2006 #6
    I'd say you're pretty accurate. :) http://i74.photobucket.com/albums/i276/navneeth/arches.jpg [Broken].Of course, as you can see, I just joined two points somewhere around the end of the arches, and it is not accurate. If you're using Google Earth you should be able to activate the scale from Tools->Options and use the Ruler (look at the button in the toolbar).
    Last edited by a moderator: May 2, 2017
  8. Nov 10, 2006 #7


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