# Example 8

## Goal

Your goal in this example is to linearize the functional model for azimuth.

## Situation

We first considered the measurement of azimuth in Example 3 where we imagined an observed azimuth from unknown station to unknown station in a planar 2D coordinate system, and we derived the following functional model:

or:

This situation is shown below.

It turns out that we need to handle things more carefully that the above simple equation will allow in cases where point does not lie northeast of point , as suggested by the following figure.

## Problem

So, building on this example, I want you to consider the more general situation shown in the figure below. That is, the case where azimuth is given by:

or:

And I want you derive the linearized functional model for this example in the form .

I want you to be as explicit in doing so as we were in Example 6, e.g. by: sketching the situation; stating what is given; stating what is required; showing your work and which equations you use; and putting boxes around your final answers.

You can / should carry the term throughout.

And to keep things simple, you may assume we only measure the azimuth once.