I am trying to write a formula in ActionScript 3 that will give me var "z" (please see image below) in degrees, which I will then convert to radians.
I will already know the value of vars "x" and "y". Using trigonometry, how can I calculate the length of the hypotenuse and therefore the variable angle of var z? A solution in either AS3 or psuedocode would be very helpful. Thanks.
What you need is this:
var h:Number = Math.sqrt(x*x + y*y);
var z:Number = Math.atan2(y, x);
That should give you the angle in radians, you might need to swap x/y and possibly add or remove 90 degrees but it should do the trick! (Note that you don't even need h to get z when you're using atan2)
I use multiplication instead of Math.pow() just because Math is pretty slow, you can do:
var h:Number = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
And it should be exactly the same.
z is equivalent to 180 - angle of yH. Or:
180 - arctan(x/y) //Degrees
pi - arctan(x/y) //radians
Also, if actionscript's math libraries have it, use arctan2, which takes both the x and y and deals with signs correctly.
The angle you want is the same as the angle opposed to the one wetween y and h.
Let's call a the angle between y and h, the angle you want is actually 180 - a or PI - a depending on your unit (degrees or radians).
Now geometry tells us that:
cos(a) = y/h
sin(a) = x/h
tan(a) = x/y
Using tan(), we get:
a = arctan(x/y)
As we are looking for 180 - a, you should compute:
180 - arctan(x/y)
