Find all possible locations for third point of triangle on Cartesian plane.

[yovelcohen]

I have a triangle on the cartesian plane with several known parameters.
e.g:
A = (1,1)
B = (4,3)
C =?
angle BAC = b = 75 deg

How can I find the location of C with these parameters?

 

[Deleted member 4993]

I have a triangle on the cartesian plane with several known parameters.
e.g:
A = (1,1)
B = (4,3)
C =?
angle BAC = b = 75 deg

How can I find the location of C with these parameters?

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.

According to the figure attached:

angle ABC = b..................... Not BAC

Which angle is 75^o?

 

[yovelcohen]

I can't seem to find the edit button on the question itself.

I made a mistake, my known angle c(ACB) not b (ABC).

basically this is for a project in python I'm writing, that uses two known locations on the cartesian plane and the angle with the third point.

I want to get all points in the range 50-150 degrees, I gave 75 deg as an example.

once I'll get a formula that can find that point, I want just to change the angle parameter and get all the points I need and run some further checks and functions on said points.

 

[Dr.Peterson]

I have a triangle on the cartesian plane with several known parameters.
e.g:
A = (1,1)
B = (4,3)
C =?
angle BAC = b = 75 deg

How can I find the location of C with these parameters?

One reason we need to see either your work, or the context of your question, is that there are various ways this could be worked out, and we would want to help you use the methods or concepts you have learned, rather than something you know nothing about. Can you use vectors? Trigonometry? If this is from a textbook or course, what topics is it likely to be intended to give you practice with?

I would start by thinking informally about what the answer should look like (as a sketch, for example), and then think about what methods might help me figure out the details.

 

[yovelcohen]

First of all, thanks!
Second,
This project is not in under anything like school,course... It's my own idea and for me.
I know a little about vectors.
But for me, the all point is learning, my main focus is about the programming process and not the math process.
This is why I just want a formula, because I know what I want to do with that information.
The idea is to get/formula, translate to code and use it in further calculations which are not relevant here.

 

[Dr.Peterson]

I presume you have thought enough about the problem to see graphically where the (infinitely many) possible points C would lie. Where will they be?

The next question would be, what form would you want the answer to be? It will not be a single pair of coordinates; would you like to find the equation of a line or two, or a parametric form, or perhaps the point that fits your description and some additional parameter, such as the distance from AB? You haven't yet specified what you want a formula to produce, which is necessary for programming.

 

[Deleted member 4993]

I presume you have thought enough about the problem to see graphically where the (infinitely many) possible points C would lie. Where will they be?

The next question would be, what form would you want the answer to be? It will not be a single pair of coordinates; would you like to find the equation of a line or two, or a parametric form, or perhaps the point that fits your description and some additional parameter, such as the distance from AB? You haven't yet specified what you want a formula to produce, which is necessary for programming.

That is the main problem - "hunting for formula/e" without knowing (caring to know) what those should look like and where did those come from!!

 

[yovelcohen]

That is the main problem - "hunting for formula/e" without knowing (caring to know) what those should look like and where did those come from!!

this is hardly the situation,
this is my way to go about problems.
I don't have the answer, I think about the answer I want to have and break it apart.
the formula I'm looking for here is just the tip of my work so far,
everything I learn, I learn this way, I'm dealing with maps and plotting on them, so far, just from this project alone I've learned so much.
I'm finding the solutions I need and then I tear them down so I can understand them, every question I ask/ answer on forums, I always like to give/receive a deep explanation as possible.

 

[yovelcohen]

I presume you have thought enough about the problem to see graphically where the (infinitely many) possible points C would lie. Where will they be?

The next question would be, what form would you want the answer to be? It will not be a single pair of coordinates; would you like to find the equation of a line or two, or a parametric form, or perhaps the point that fits your description and some additional parameter, such as the distance from AB? You haven't yet specified what you want a formula to produce, which is necessary for programming.

I don't have a lot more parameters to give.

I want to get all the points that create an angle of between 50-150 degrees with both A and B.
one other parameter I thought of is that if the distance AB = x,
and O = mid AB,
then the distance AO must be 2x.

that's all the parameters I have;
A,B,dis AB,O,dis AO, angle ACB.

 

[Dr.Peterson]

I don't have a lot more parameters to give.

I want to get all the points that create an angle of between 50-150 degrees with both A and B.
one other parameter I thought of is that if the distance AB = x,
and O = mid AB,
then the distance AO must be 2x.

that's all the parameters I have;
A,B,dis AB,O,dis AO, angle ACB.

First, now that you're no longer being moderated, we can interact better (and you should be able to edit).

Looking back to what you wrote before I wrote, but I couldn't see yet, I see that you made a huge mistake in the OP -- the given angle is neither BAC nor b, as you wrote, nor ABC as you drew, but ACB, which is at the unknown point rather than one of the known points! In the original problem as you had stated it, C would lie on one of two rays from B (or A), at the given angle, and we would need to find the equation of each line (and then present it in whatever way would be helpful to you). That is not at all the case in what you really want.

There is an important geometry theorem you need to know, that any angle inscribed in a circle is equal to half the arc it cuts from the circle. A consequence of that is that given the angle at C, you know that C lies on one of two particular circles through A and B. We can find the centers of those circles. But I'm going to hold off on that.

We still need to figure out what you really want to find. You can't find, all at once, ALL possible locations of C, though that is still what you are claiming to want. You need to decide what you are going to do with the result, in order to have any idea what the output of the function you want to write would be.

Now, what you just said in post #9 doesn't make much sense. If you know the locations of A and B, then the distance AB and the location of the midpoint O are easily determined -- they are not additional information. And the distance AO would not be 2x; it would be x/2, and again would tell us nothing new about the location of C. Either I am totally misunderstanding what you want to do, or you have not thought about the reality of your goal, such as by drawing a figure.

Here is what it looks like:



Point C can lie anywhere on the part of the red circle above AB, or any part of the green circle below AB. (My O is the center of the red circle.)

Now, in practice, you surely want to choose one of those possible points. How do you plan to do that? That will be part of what we need in order to specify the actual requirements for whatever formula or procedure we come up with.

You've hinted at the context of your question (something about maps?); when you ask a question, it's really valuable if you can explain the context fully enough to make it clear what you will be doing with the result. It's very common for people to think that by removing a question from its context they are making it easier for helpers, but the truth is the opposite. The more you tell us, the more quickly we can discern your needs and help appropriately.