What is the back azimuth of 223 degrees?

Answer 1

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.