MEASUREMENT OF ANGLES

      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.