College Algebra & Trigonometry, 2018a

344 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY
8.1 Measuring Angles
Measuring Angles in Degrees
The two most common units for measuring angles are degrees and radians. Degrees
are based on the ancient Mesopotamian assignment of 360 ◦ to a complete
circle. This has its origin in the division of the horizon of the nighttime sky as
the earth takes 365 days to travel around the sun. Because degrees were originally
developed by the Mesopotamians, they are often also broken out into 60
unit measures of minutes and seconds. Sixty seconds make one minute and sixty
minutes makes one degree.
60 seconds=1 minute
or
60 ′′ =1 ′
60 minutes=1 degree
or
60 ′ =1 ◦
Angles measured in degrees may also be expressed using decimal portions of a
degree, for example:
72.5 ◦ =72 ◦ 30 ′
Converting from decimal to DMS
Converting between degrees expressed with decimals and the degrees, minutes,
seconds format (DMS) is relatively simple. If you’re converting from degrees
expressed with decimals to DMS, simply take the portion of the angle behind the
decimal point and multiply by 60. In our previous example, we would take the .5
from 72.5 ◦ and multiply this by 60: 0.5*60=30. So, the angle in DMS units would
be 72 ◦ 30 ′ .