MEASUREMENT OF ANGLES: DIFFERENT SYSTEMS
Having
defined an angle, it is now necessary to find a convenient unit for measuring
angles. For different practical purpose, different suitable units are used for
the measurement of angles.
Since a right
angle is an angle of constant magnitude, it can be conveniently used as our
unit for the measurement of angles. But for many purposes right angle is too
big a unit, hence smaller unites are obtained from aright angle.
THERE ARE THREE SYSTEMS FOR MEASURING ANGLES, VIZ.,
(1) SEXAGESIMAL
SYSTEM,
(2)
CENTESIMAL SYSTEM,
(3) CIRCULAR SYSTEM.
SEXAGEMISAL OR ENGLISH SYSTEM
The most commonly used system for
measuring angles is the sexagesimal system, which is also known as the common
system or English system or degree system. the principal unit in this system is
degree which is one-ninetieth part of right angle. A degree is divided into 60
equal parts and each part is called a minute (‘). A minute is again divided
into 60 equal parts and each part is called a second (“).thus
1
right angle (rt. Degree) = 90 degrees
1
degree =60 sexagesimal minutes (60’)
1’=60
sexagesimal seconds (60”)
Note Right
angle is not a unit of the system.
CENTESIMAL
OR FRENCH SYSTEM
The
principal unit of this system is grade (&), which is one-hundredth part of
a right angle. One grade is equal to 100 minutes (‘) and one minute is equal to
100 seconds (“). Thus
1rt.
Angle =100 grades (100&)
1&
=100 centesimal minutes (100’)
1’
= 100 centesimal seconds (100”)
This system
was first proposed in France
but the attempt to introduce the system was not successful.
Note : Minute
and seconds of sexagesimal system are not the same as the centesimal minutes
and seconds. For example,
1 rt. Angle = 90*60 sexagesimal minutes
=100*100
centesimal minutes.
CIRCULAR SYSTEM OR REDIAN SYSTEM
In advanced mathematics, the most
convenient system for the measurement of angles is the circular or radian
measure.
RELATION BETWEEN SEXAGESIMAL AND CENTESIMAL SYSTEMS
To
convert the measure of an angle in degree to grades:
Let
D be the number of degrees in an angle.
since 90 degree = 1 rt. Angle, and 100& =1 rt. Angle,
So 90 degree = 100 grades
Or 1 degree =100/90
grades =10/9 grades.
Hence D degrees = 10/9 D grades.
To
convert the measure of an angle in grades to degrees:
LET
G be the number of grades in an angle.
Since 100 grades = 1 rt. Angle, and 90 degree =1rt. Angle,
So 100grades = 90 degrees
Or 1 grade
=90/100degree = 9/10 degree
Hence G degree = 9/10g degrees.
