Study About Grade Measure

Introduction of study about grade measure:
Grade measurement is the geodetic determination of the local radius of curvature of the figure of the Earth by determining the difference in astronomical latitude between two locations on the same meridian, the metric distance between which is known.

The first known grade measurement was performed by Eratosthenes (240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The Dutch geodesist Snellius (~1620) repeated the experiment between Alkmaar and Bergen op Zoom using more modern geodetic instrumentation.

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More about the grade measure:


In trigonometry, following three systems are used for measuring an angle according to different units employed:

Sexagesimal system.

Centesimal system

Circular system.

Centesimal system is used to measure a grade.

Centesimal system:

In this system, an angle is measured in terms of grades, minutes and seconds. Thus we have

1 right angle    =          100 grades (100g).

So        90 angle           =          100 grades (100g).

1 angle             =          1.111 grade (1.111g).

1 grade             =          100 minutes (100’).

1 minute          =          100 seconds (100’’).

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Example problem for grade measure:


Find the degree grade corresponding to the following time and angle measures:

a)      270 angle

b)      1 hour 40 minutes

c)      3 hour 20 minutes

d)     1 hour 40 minutes

e)      120 angle

Pro 1:    270o angle = grade?

Sol :     270 angle         =270 x 1.111  (where 1 = 1.111)

=299.97

After routing resultant number, we get

=300

270o angle or right angle = 300 grade (200g)

Pro 2 :      3 hour 20 minutes

Sol :               1 hour = 60 minutes

So 3 hour 20 minutes = 180 minutes+20 minutes

We know 1 grade = 100 minutes, so we can rewrite the given as

3 hour 20 minutes = 180 minutes + 40 minutes

= `300/100` grade

= 3 grades

=3 grades (3g)

3 hour 20 minutes is equal to 3 grades (1g)

Pro 3:          1 hour 40 minutes

Sol :            1 hour = 60 minutes

So 1 hour 40 minutes = 60 minutes+40 minutes

We know 1 grade = 100 minutes, so we can rewrite the given as

1 hour 40 minutes = 60 minutes + 40 minutes

= 100/100 grade

= 1 grade

=1 grade (1g)

1 hour 40 minutes is equal to 1 grade (1g)

Pro 4:       Find the 120 angle into grades?

Sol :       120 angle         =120*1.111

=133.32

After routing resultant number, we get

=133 grades (133g)

120 angles are equal to 133 grades (133g)