Trigonometry, calculate angel between three coordinates

[gedas]

hey,

i have got three sets of x an y coordinates , where one of the x y coordinates keeps on changing all the time.
lets say i have first set where the coordinates are int x=100 and int y=100;
second set would be : int x=100; int y=150; but the last set of coordinates would always change.

so if we would draw a line from the first set to the second set and from second set to the changing third set and back again to the first set of coordinates i would get a triangle.

what i want is to get the angel of the triangle which would show the degrees from the first set of points to the changing points.

i know i have to use one of the following: sin, cos or tan, but my trigonometry skills are very rusty.

i hope someone could help me or suggest me anything that would lead me to the right direction of solving this issue.

any help is greatly appreciated!!

THANK YOU

[Ezzaral]

You need to use one of the inverse functions: acos, asin, or atan from Math. Which one depends on which sides you compute the line lengths for.

Edit: If you've forgotten which sides relate to which function, Wikipedia has a graph and table here: http://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions

[gedas]

well i am going to know the line length for all the lines.
the shape would look something like this (shape b)
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i5/s5q1.gif

left side of the triangle will keep on changing (slightly) due to the change of the coordinates. how could i calculate the angel of the top side of the triangle(like show in the image above).

Thank you

[Ezzaral]

Since they're not right triangles, using the dot product of the vectors may be easier.
Given the vectors (x1,y1) and (x2,y2):
angle in radians = arccos((x1*x2 + y1*y2) / ( sqrt(x1*x1 + y1*y1) * sqrt(x2*x2 + y2*y2) )

More wiki info here: http://en.wikipedia.org/wiki/Dot_product#Geometric_interpretation

Pretty decent vector algebra reference here:
http://emweb.unl.edu/math/mathweb/vectors/vectors.html#vec4

Edit: You may need to twiddle the signs a bit. I'm not a vector math genius and always have to "play" with the numbers a little.

[gedas]

thank you!!! this formula looks like it would work,but my amateur programming skills are stopping me on implementing "arccos".
i have tried Math.arccos(......); but it gives me error, that the symbol can not be found
what should i do to get rid of this error??

thanks again for your reply

[Ezzaral]

The method is Math.acos() Remember that the angle is in radians. You can use Math.toDegrees(double) to convert to degrees if you need to.

[gedas]

sorry for the previous post,ignore it please i have worked it out and it is simply Math.acos();
but the calculation gives me wrong values i convert everything back to degrees

degrees = (radians * 180 / Math.PI)

but for some reason the output i receive varies from 0- 15 instead of 0-360 degrees. i am not sure what would be wrong in the calculation...
maybe im doing something wrong.

thank you for your help!!

[Ezzaral]

It may depend on how you represented your input vectors. For that upper point on figure b that you refered to, you would need to calculate the vectors from that point of origin such that they were pointing out and down from that position using (x2-x1,y2-y1).

Here's a small spreadsheet of the results I got with that formula. I calc'd the angle between each vector pair on an irregular triangle I just made up. The total of all calculated inner angles was 180 and each one seemed to be right by visual estimation (the lower row is degrees, I forgot a label)

[Ezzaral]

You could take a look at Law of Cosines as well, if the vector method isn't working out for you. It's just another way to skin the same cat.

[gedas]

Thanks a lot for all the help it really did help me !!
i managed to solve my problem from the example in the wiki.
i knew all the length of all the sizes so all i had to do is work out the angel.

hypotenuse  = Math.sqrt(Math.pow(xb-xa,2) + Math.pow(yb-ya,2));
       adjacent    = Math.sqrt(Math.pow(xa-xa,2) + Math.pow(ya+50-ya,2));
       oposite     = Math.sqrt(Math.pow(xb-xa,2) + Math.pow(yb-(ya+50),2));
       radians = Math.acos((Math.pow(adjacent,2) + Math.pow(hypotenuse,2)- Math.pow(oposite,2)) /(2*adjacent*hypotenuse));

thank you once again, you have been really helpful !

[saranyabaskaran]

hai...
me to working in the same area...i couldnot understand how to set the angle between three points in java...could u plz help me...

thank u...

[Ezzaral]

@saranyabaskaran: No, do not hijack other posters threads to ask your own questions. Please start a new thread of your own and explain more clearly what you are trying to do when you say "set the angle".