Convert the following Azimuths to Bearings
a. 166 degrees 06 minutes 06 seconds.
b. 125 degrees 25 minutes 24 seconds
c. 169 degrees 16 minutes 16 seconds.
d. 180 degrees 01 minutes 61 seconds.
The correct answer and explanation is :
To convert azimuths to bearings, follow a rule-based method that considers which quadrant the azimuth angle falls into. Bearings are always expressed as angles from north or south toward east or west, within a range of 0° to 90°.
Conversions:
a. 166° 06′ 06″
Since 166° is between 90° and 180°, it lies in the Southeast (SE) quadrant.
Bearing = S (180° − Azimuth) E
180° − 166° 06′ 06″ = 13° 53′ 54″
✅ Bearing = S 13° 53′ 54″ E
b. 125° 25′ 24″
125° is also between 90° and 180° → SE quadrant.
180° − 125° 25′ 24″ = 54° 34′ 36″
✅ Bearing = S 54° 34′ 36″ E
c. 169° 16′ 16″
Also between 90° and 180° → SE quadrant.
180° − 169° 16′ 16″ = 10° 43′ 44″
✅ Bearing = S 10° 43′ 44″ E
d. 180° 01′ 61″
First, simplify the seconds and minutes.
61″ = 1′ 1″ → 01′ + 1′ = 02′, 1″ remaining
So, it’s 180° 02′ 01″
Since it’s slightly more than 180°, it’s in the Southwest (SW) quadrant.
Azimuth − 180° = 02′ 01″
✅ Bearing = S 02′ 01″ W
300-word Explanation:
Azimuth is a type of angle measurement that starts from true north and increases clockwise, ranging from 0° to 360°. In contrast, a bearing is a direction expressed as an angle measured from north or south toward the east or west, with a maximum value of 90°.
To convert azimuths to bearings, it is crucial to identify the quadrant the azimuth falls in:
- 0° to 90°: NE quadrant → Bearing = N Azimuth E
- 90° to 180°: SE quadrant → Bearing = S (180° − Azimuth) E
- 180° to 270°: SW quadrant → Bearing = S (Azimuth − 180°) W
- 270° to 360°: NW quadrant → Bearing = N (360° − Azimuth) W
For each problem above:
- Parts a, b, and c are all between 90° and 180°, so they are in the SE quadrant, and the formula S (180° − Azimuth) E was used.
- Part d is slightly above 180°, placing it in the SW quadrant, requiring the formula S (Azimuth − 180°) W.
Additionally, it’s important to handle angles properly by simplifying seconds over 60 to minutes, and minutes over 60 to degrees when needed. For instance, in part d, “01′ 61”” becomes “02’ 01”” by carrying over 60 seconds into a minute.
This method ensures accurate conversions critical in navigation, land surveying, and engineering.