Calcing length of object using trig

In summary, the individual is trying to find the dimensions of the Freedom Arches at Nathan Phillips Square using Google Earth. They have tried to estimate the length using pixels and distance, but are struggling to figure out the angle needed for accurate calculations. They mention the possibility of using a known object on the map, such as the Skydome, to measure and compare. Based on their calculations and a provided image, the approximate length of the arches is 114 feet.
  • #1
DaveC426913
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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 realize 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?
 
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  • #2
I guess the one thing Google Earth does not have is a legend, showing linear feet on the map!

Linear feet?

tan(angle) = height/base
 
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  • #3
neutrino said:
Linear feet?
Well, you know what I mean.

neutrino said:
tan(angle) = height/base
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.
 
  • #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 length of arch itself once you know the base length and equation of the arc(h). :biggrin:
 
  • #5
neutrino said:
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 length of arch itself once you know the base length and equation of the arc(h). :biggrin:
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.)
 
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  • #6
I'd say you're pretty accurate. :) http://i74.photobucket.com/albums/i276/navneeth/arches.jpg .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).
 
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  • #7
Oh!
10char
 

1. How do you determine the length of an object using trigonometry?

To determine the length of an object using trigonometry, you will need to use the trigonometric functions of sine, cosine, and tangent. You will also need to know the angle between the object and your line of sight, as well as the distance between you and the object. By using the trigonometric ratios, you can calculate the length of the object using basic geometry principles.

2. What is the difference between using the sine and cosine functions in calcing length?

The main difference between using the sine and cosine functions in calcing length is that the sine function will give you the length of the side opposite to the given angle, while the cosine function will give you the length of the adjacent side. This is why it is important to know the angle between your line of sight and the object in order to use the correct trigonometric function.

3. Can you use trigonometry to calculate the length of any object?

Yes, you can use trigonometry to calculate the length of any object as long as you have the necessary information, such as the angle and distance between you and the object. Trigonometry is a fundamental tool in geometry and can be used to solve various problems involving lengths, angles, and distances.

4. What are some real-world applications of calcing length using trigonometry?

There are many real-world applications of calcing length using trigonometry, such as determining the height of a building or the width of a river. It is also used in navigation, surveying, and astronomy. Trigonometry is an essential tool in many fields, including engineering, physics, and architecture.

5. Is there a specific formula for calcing length using trigonometry?

Yes, there is a specific formula for calcing length using trigonometry. It is known as the law of sines, which states that the ratio of the length of a side to the sine of the opposite angle is equal for all sides of a triangle. There is also the law of cosines, which relates the length of a side to the cosine of the adjacent angle and the length of the other two sides. These formulas can be used to calculate the length of any object using trigonometry.

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