Convert the following Bearing’s to Azimuth’s
a. N 40 degrees 45 minutes 32 seconds W
b. S 24 degrees 10 minutes 25 seconds E
c. N 87 degrees 44 minutes 00 seconds W
d. S 25 degrees 25 minutes 60 seconds E
The correct answer and explanation is :
To convert bearings to azimuths, we follow a simple set of rules based on the quadrant in which the bearing lies. Azimuths are measured in degrees clockwise from due north (0° to 360°).
Given Bearings and Their Azimuths:
a. N 40° 45′ 32″ W → Azimuth = 360° – 40° 45′ 32″ = 319° 14′ 28″
b. S 24° 10′ 25″ E → Azimuth = 180° + 24° 10′ 25″ = 204° 10′ 25″
c. N 87° 44′ 00″ W → Azimuth = 360° – 87° 44′ 00″ = 272° 16′ 00″
d. S 25° 25′ 60″ E → (Note: 60 seconds = 1 minute, so this is S 25° 26′ 00″ E)
→ Azimuth = 180° + 25° 26′ 00″ = 205° 26′ 00″
Explanation (300+ words):
Bearings describe direction using the compass quadrants: Northeast (NE), Southeast (SE), Southwest (SW), and Northwest (NW). They always start with either “N” or “S” and are followed by an angle (from 0° to 90°) and a final direction “E” or “W.” For example, N 40° W means 40 degrees west of north.
On the other hand, azimuths are measured clockwise from true north, ranging from 0° to 360°, with no reference to cardinal directions. Therefore, conversion from a bearing to an azimuth depends entirely on the quadrant the bearing lies in.
Here’s a breakdown by quadrant:
- NE quadrant (N … E): Azimuth = the bearing angle itself.
- SE quadrant (S … E): Azimuth = 180° + the bearing angle.
- SW quadrant (S … W): Azimuth = 180° + the bearing angle.
- NW quadrant (N … W): Azimuth = 360° – the bearing angle.
Let’s apply this to each case:
- a. Bearing is in the NW quadrant → Azimuth = 360° – angle
→ 360° – 40° 45′ 32″ = 319° 14′ 28″ - b. Bearing is in the SE quadrant → Azimuth = 180° + angle
→ 180° + 24° 10′ 25″ = 204° 10′ 25″ - c. NW again → Azimuth = 360° – 87° 44′ 00″ = 272° 16′ 00″
- d. SE quadrant again (corrected to 25° 26′ 00″)
→ Azimuth = 180° + 25° 26′ 00″ = 205° 26′ 00″
Understanding how bearings convert to azimuths is critical in fields like land surveying, navigation, and GIS, where precise direction is essential for plotting and mapping.