Calculating Azimuth from Variables: dX, dY & Angle

[StarFire]

Homework Statement

Ok, I'm doing a survey course, and I need to calculate the azimuth of an angle. The 'textbook' is a series of not-all-that-well-written notes, so I'm hoping you can help (it tells me that to calculate azimuth I need to reduce to absolute coords, but in order to do so I need the azimuth! ).

I'm not going to post my variables because I don't want you to give me the answer, only to help me figure out the formula I need. I know this is basic trig, but it's been decades since I've studied any trig or physics. I know what an azimuth is, just not how to calculate it from my data.

I know one angle, and the distance between my station point (A) and the point I'm measuring (B). I know the angle is zero because I set the instrument to zero along it.

http://www.tfw2005.com/boards/members/starfire_mk2-42816-albums-misc-retribution-files-picture1583-01.jpg

I know point B is in the 4th quadrant, with -dX and +dY values. Intuitively, this means my AZ will be ~ the 300* range. Problem is, while I understand both the rectangular and polar coord systems (I suspect this is a polar coord system I'm working in, since I have a -dX angle), I don't know how to calculate dX and dY.

Homework Equations

Polar angle theta =tan minus 1 (dX/dY) +addition constant

If this is the right formula, how do I calculate dX and dY??

The Attempt at a Solution

 

[LowlyPion]

Welcome to PF.

Sounds like your 0 line is known, so your azimuth angle to your object in question sounds known as well. (The angle from that line to the line pointing at B.)

To transform coordinates:
http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations#2-Dimensional

So if you know θ and r, looks like you can transform that to x,y.

 

[nlightner]

To calculate the azimuth of an angle, you will need to use the trigonometric functions of tangent and inverse tangent. The formula you provided is correct, however, dX and dY are not calculated separately but are used together in the formula.

To calculate dX and dY, you will need to use the distance between your station point (A) and the point you are measuring (B). This can be done using the Pythagorean theorem: d = √(dX^2 + dY^2), where d is the distance between A and B.

Once you have calculated the distance, you can then use the tangent function to find the angle theta, which is the azimuth. The formula for tangent is: tanθ = dY/dX. This will give you the value of theta in radians.

If you need the angle in degrees, you can convert it by multiplying the value in radians by 180/π (pi).

I hope this helps you in calculating the azimuth from your variables. Remember to double check your calculations and make sure your units are consistent. Good luck with your survey course!