Azimuth and Bearings: Calculate the smaller angles between these directions.  North 78 Degrres 25 Minutes and 30 Seconds and Azimuth is 92 Degress 11 minutes and 50 seconds????

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember that you may either evaluate the angle between two azimuths, or the angle between two bearings, hence, you need to convert the bearings in azimuths.

You should remember that if the bearing is in the northeast quadrant yields that the azimuth and the bearing have the same values, hence `N 78^o 25' 30'' E = AZ 78^o 25' 30''.`

If you need to find the azimuth in the southeast quadrant, you need to subtract the value of bearing from `180^o` , such that:

`180^o - S 78^o 25' 30'' E = AZ 121^o 34' 30''`

If you need to find the azimuth in the southwest quadrant, you need to add the value of bearing from `180^o` , such that:

`180^o + N 78^o 25' 30'' W = AZ 258^o 25' 30''`

If you need to find the azimuth in the northwest quadrant, you need to subtract the value of bearing from `360^o` , such that:

`360^o - N 78^o 25' 30'' W = AZ 281^o 34' 30''`

You should find the smaller angle between two azimuths, hence, you need to perform the subtraction between the smaller and larger angles, such that:

`AZ 78^o 25' 30'' - AZ 78^o 25' 30'' = 0^o`

`AZ 121^o 34' 30'' - AZ 78^o 25' 30'' = 43^o 9'`

`AZ 258^o 25' 30'' - AZ 78^o 25' 30'' = 180^o`

`AZ 281^o 34' 30'' - AZ 78^o 25' 30'' = 203^o 9'`

Hence, evaluating the smallest angle between two azimuths, yields that this angle is obtained if they are in the Northeast quadrant.