Sexagesimal System

In sexagesimal system, the angle that the rotating ray traces making one complete revolution is taken to be 360°.

One-fourth of it is 90°, that is, one right angle 90°and 1/90th part of a right angle is 1°. The other lower units of this system are minute and second.

The following table of sexagesimal system shows the relation between them.

1 right angle = 90 degrees or 90°

1° = 60 minutes or 60’

1’ = 60 seconds or 60”


Worked-out examples on how to express the sexagesimal system in degree, minute and second:

Express 85.12° in degree, minute and second.

Solution:

85.12° = 85° + (0.12)°

= 85° + (0.12 × 60)’ [Since, 1° = 60’]

= 85° + 7.2’

= 85° + 7’ + (0.2)’

= 85° + 7’ + (0.2 × 60)”

= 85° + 7’ + 12”

Therefore, 85.12° = 85° 7’ 12”

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