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!
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:
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.
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: .
. . 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.
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 :/