Can latitude and longitude be Cartesian coordinates at small scale?

[Zermelo]

Hello, the title/question is self explanatory:
If I have some latitude/longitude coordinates (which I know represent angles), let’s say (41.6284828, 54,73748), and (41.6284591, 54.73719), can I use them as points in the Cartesian plane? For example, can I compute the line connecting them with the formula y-y1 = k(x-x1)? Keep in mind that I’m only talking about really small distances, under 100 meters.
If I can’t do this due to the fact they are angles, I’m thinking about fixing one of the points (x1, y1) as the coordinate beginning (0, 0), and computing the distance of the second point (x2, y2) from points (x1, y2) and (x2, y1) (using known formulas for this, such as the Haversine formila), and thus getting the Cartesian x and y coordinates of the point. Is this ok?

 

[Dr.Peterson]

If you know about the haversine formula, then you surely know that distances, even on a small scale, are not scaled the same relative to latitude and longitude; the relevant circles have different radii. But if you scale appropriately, to convert angles to distances, then you can locally use the results like xy coordinates.

So what you suggest will work for finding points on a line (since the scales don't have to match for that); but it will not work for distances in different directions (for which they do have to match).

 

[Zermelo]

If you know about the haversine formula, then you surely know that distances, even on a small scale, are not scaled the same relative to latitude and longitude; the relevant circles have different radii. But if you scale appropriately, to convert angles to distances, then you can locally use the results like xy coordinates.

So what you suggest will work for finding points on a line (since the scales don't have to match for that); but it will not work for distances in different directions (for which they do have to match).

Thanks for the answer! But could you help me out a little bit more? Here is my acutal task:
I have 3 (lng, lat) points from which I want to construct a triangle, and then measure the distance of a fourth point to that triangle. So, I basically want to turn those 4 points to points in the Cartesian plane, and then measure some distances. Will my method work for this? And what do you mean by "if you scale appropriately"? Keep in mind that I don't need exact distances, but approximations. Thanks again, and sorry for the hassle!
EDIT: unfortunately, I know only about the Haversine formula, don't know much about the details..

 

[Dr.Peterson]

Here is a post on my blog that deals with planar approximations (with a link to a post about the haversine formula).

Distances along a meridian are equal to the radius of that great circle (i.e. of the earth) times the (radian) angle. Distances along a parallel of latitude are calculated using the radius of that parallel, which is the cosine of the latitude times the radius of the earth. That's the scaling I referred to. Once you've converted angles to distances, you can (approximately) use them as (x,y).

But how do you define the distance of a point to a triangle?

 

[Zermelo]

Here is a post on my blog that deals with planar approximations (with a link to a post about the haversine formula).

Distances along a meridian are equal to the radius of that great circle (i.e. of the earth) times the (radian) angle. Distances along a parallel of latitude are calculated using the radius of that parallel, which is the cosine of the latitude times the radius of the earth. That's the scaling I referred to. Once you've converted angles to distances, you can (approximately) use them as (x,y).

But how do you define the distance of a point to a triangle?

Great, thank you very much!!!
I actually posted another thread about the distance of a point to a triangle. I believe it should be defined as the minimum distance of the point from any point on the triangle. In some cases that would be the distance from the side of the triangle, and in others the distance from the vertices.

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