Thread: Get angle from coordinates of a corner?

Hi, please bear with me as I have not taken trig in over 10 year.. I am PRETTY sure this is a trigonometry problem.

Here is an image that describes my problem:


Note: the lengths and angles indicated may not be 100% exact, but they should be close. I measured them as well as I was able. The lengths on the labelled sides ARE the same on all the shown triangles, and do not change. The values for X and Y ARE known, and X does not change either.

I need an expression that describes the value for Z in terms of X and Y.

Any help on this would be appreciated, I don't really even know where to start!

Originally Posted by Malkalypse

Hi, please bear with me as I have not taken trig in over 10 year.. I am PRETTY sure this is a trigonometry problem.

Here is an image that describes my problem:


Note: the lengths and angles indicated may not be 100% exact, but they should be close. I measured them as well as I was able. The lengths on the labelled sides ARE the same on all the shown triangles, and do not change. The values for X and Y ARE known, and X does not change either.

I need an expression that describes the value for Z in terms of X and Y.

Any help on this would be appreciated, I don't really even know where to start!

i don't see Z labeled on the actual figure, i have no idea what length or angle it is you want to find

Sorry if I was not clear about that.. Z here describes the angle that is labelled (where it says Z1, Z2, and Z3)

Basically, I need an expression for the angle of the indicated corner as shown in this link:
http://www.versatileartist.com/temp/pca_help.avi

to be more specifically clear about the original image: X is the distance directly right from the bottom corner of the triangle, Y is the distance directly up from it, and Z is the angle of the top corner. X does not change.

Hello, Malkalypse!

If I interpret the problem correctly, angle z = angle CBA.

I assume that the are fixed
. . and that may vary.

Code:

                            B
                            *
                        *  *|
                     *  z * |
        14.776    *      *  |
               *        *   |
            *          *    |
         *            *     |
    C *              *      |y
       *            *       |
        *          *_____   | 
         *        *√x²+y²   |
  14.967  *      *          |
           *   *            |
            * *             |
             *- - - - - - - *
             A       x      O

In right triangle , we have: .
. . Hence: .

From the Law of Cosines: .

. . so we have: .


Since

. . we have: .

Hm, doesn't seem to work for some reason.. maybe I'm doing it wrong.

Also, I realized that what I really need is angle CBO.. though I should be able to get that by adding CBA and ABO...

My distances were also inaccurate (I wanted to make sure all my information was correct so I checked again). AC is 14.9921 and CB is 14.8591.

However, even taking all this into account, I can tell that the answers I'm getting aren't even close.I don't know if it's maybe an order of operations issue, but I seem to be ending up with numbers less than 1, which isn't right.

---
You know what, I just realized that I am rustier than I even thought. When you say "cos z = ..." ... does that mean "the cosine of z = ..." or that "z as a cosine = ..." or just "z = ..." and is that answer in radians or degrees? :P
Sorry for asking stupid questions, but I really need to figure this out.

Originally Posted by Malkalypse

You know what, I just realized that I am rustier than I even thought. When you say "cos z = ..." ... does that mean "the cosine of z = ..." or that "z as a cosine = ..." or just "z = ..." and is that answer in radians or degrees? :P
Sorry for asking stupid questions, but I really need to figure this out.

it means the cosine of z

Okay, so how do I convert it to degrees?

Sorry if I seem like an idiot, but it really has been a long time since I have done anything like this. In the meantime, I'm trying to get a very stubborn program to use this information, and it would be a lot easier if I were sure that the the information I am putting in is correct :/

Originally Posted by Malkalypse

Okay, so how do I convert it to degrees?

Sorry if I seem like an idiot, but it really has been a long time since I have done anything like this. In the meantime, I'm trying to get a very stubborn program to use this information, and it would be a lot easier if I were sure that the the information I am putting in is correct :/

are you using a calculator? if so, just put it in degrees mode when doing the computations. if you're using some other program, well, i don't know. it depends on how the program works

Originally Posted by Malkalypse

Okay, so how do I convert it to degrees?

Convert what to degrees? Radians?
Then use the formula,