# Using triangulation to find distance...

#### ViolentCorpse

Hi,

There's something I'm having difficulty understanding in the triangulation method of finding distances. Just trying to understand the principle.
If two objects have the same apparent size and are placed at different distances, wouldn't our measurement of angles be the same for both?
E.g the sun and moon both have an approximately equal apparent size as viewed from Earth. But the sun is much farther away than the moon is. I can't visualize how, if measurements are made, different values of angles would be attained for the two cases i.e moon and sun.

I don't know why my intuition is compelling me to believe that if the apparent sizes of two objects are same, the angles will also be the same no matter how far apart the objects are...

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#### ViolentCorpse

Dear doctor, I understand how triangulation basically works. I'm just confused when I consider that it is possible for two objects to be placed at different locations and be different sizes and yet have the same angular size. Now, if these objects are triangulated, would they both form the exact same angles, since they have the same angular size? If they do, then we will have exactly identical triangles and there distance would also turn out to be the same, which is not actually true...

#### pbuk

Dear doctor, I understand how triangulation basically works.
I don't think you do, because triangulation doesn't use the apparent size of an object - in fact if an object is not a point you need to select a fixed point on the object to use for both angular measurements.

#### ViolentCorpse

I don't think you do, because triangulation doesn't use the apparent size of an object - in fact if an object is not a point you need to select a fixed point on the object to use for both angular measurements.
Yeah I probably don't.

So, you're saying that two different objects located at different distances will form different angles (if we select a fixed point on each object for making the measurements) irrespective of their apparent size?

#### jbriggs444

Homework Helper
So, you're saying that two different objects located at different distances will form different angles (if we select a fixed point on each object for making the measurements) irrespective of their apparent size?
One way of doing triangulation is to measure the angle from a single fixed point "here" to two different points a known distance apart on an object over there. This is the principle on an old style surveyor's transit. The surveyor measures the angle to one marker high on a survey pole and the angle to another marker low on the survey pole. A little trig and *voila* -- the distance from transit to pole is known. Using this approach, the apparent size of the moon is only useful for measuring the range to the moon if you know its actual size.

The other way of doing triangulation is to measure the angle from two points a known distance apart "here" to a single object (or to a single point on an object) "over there". This is a principle behind a coincidence rangefinder (https://en.wikipedia.org/wiki/Coincidence_rangefinder). It is also the essential principle behind parallax measurements. Using this approach, the apparent size of the moon is irrelevant.

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#### FactChecker

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2018 Award
You are thinking that the left line is pointing at the left side of the distant objects and the right line is pointing at the right side of the objects. You are correct that then the angles could be the same. But if you point both lines at the left side of the objects, the closer object would make a different angle than the farther farther object. That is what you do when you triangulate. You pick a single point on the object and point both lines at that single point.

#### ViolentCorpse

Thanks a lot guys! :)

#### Stephanus

But if you only use two objects for triangulation, wouldn't there be 2 answers?
Perhaps we should use 3 objects/points for triangulation, that's why it is called triangulation.
And in 3D space we use 4 objects/points for 'triangulation'. Is this true?

#### pbuk

But if you only use two objects for triangulation, wouldn't there be 2 answers?
No, why do you think that?
Perhaps we should use 3 objects/points for triangulation, that's why it is called triangulation.
No, it's called triangulation because bearings only need to be measured from or to two different points to locate a third point - these three points form a triangle (not to be confused with the "triangle of uncertainty" when three bearings are used).
And in 3D space we use 4 objects/points for 'triangulation'. Is this true?
No, two points are still sufficient (there is one more unknown but 2 more measurements as we have elevation angles as well as direction).

#### Stephanus

But if you only use two objects for triangulation, wouldn't there be 2 answers?
No, why do you think that?
Is this why?

But it's hard to draw three pictures. Has to use some graphic software other than Microsoft Paint.

#### jbriggs444

Homework Helper
Is this why?
View attachment 87299
But it's hard to draw three pictures. Has to use some graphic software other than Microsoft Paint.
Triangulation is not about using multiple distance measurements to determine position. [That's how GPS works]. Triangulation is about using multiple angle measurements.

#### jbriggs444

Homework Helper
Oh, I'm so sorry. I was wrong. Is this like determining paralax?
Yes.

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