A BACK AZIMUTH IS A PROJECTION OF THE AZIMUTH FROM THE ORIGIN TO THE OPPOSITE SIDE OF THE AZIMUTH CIRCLE. i.e. THERE ARE 360 DEGREES IN AN AZIMUTH CIRCLE, THUS THE OPPOSITE DIRECTION IS 180 DEGREES.

As the request is for the back azimuth, then what is wanted is the reverse (or inverse) of the azimuth, 223 degrees. In other words, an object moved in the direction of 223 degrees (Southwest relatively), but now the desire is to reverse the travel in order to arrive at the starting point. (That starting point would have to be Northeast relatively.)

One does not typically work with directions exceeding 360 degrees nor less than 0 degrees as that range is the range of a compass. Therefore, the back azimuth of 223 degrees, whatever it is, must be between zero and 360 degrees.

To determine the back azimuth all that is necessary is the knowledge that 1) the back azimuth is the opposite direction of the azimuth and 2) 180 degrees either added or subtracted will yield the back azimuth, and 3) the correct back azimuth must be in the range of zero to 360 degrees.

Given this knowledge and the variable definitions Ab = Back Azimuth and A = Azimuth,

Ab = A + 180

or

Ab = A - 180

But which equation yields the correct back azimuth?

Using knowledge point #3 above, the correct result will be the one that is between zero and 360 degrees. Therefore,

Ab = A - 180 = 223 - 180 = 43 degrees

is the correct back azimuth.

The other choice, Ab = A + 180 = 223 + 180 = 403 degrees, exceeds the range of the compass, so 403 degrees cannot be the correct back azimuth.

348 degrees. It is the exact opposite on a compass dial. 168 is 12 degrees before due south, so the back azimuth is 12 degrees before due north.

Nominally 274 degrees.

But on the real, spherical earth, the farther north you are, and the farther apart

the two points are, the more the true back-azimuth will depart from 274 degrees.

An azimuth thruster is an engine and ship's propeller in a pod which is azimuth adjustable.