Question

convert the following in to sexagesimal. π/4​

Answer 1

Answer:

We know, Sexagesimal, Centesimal and Circular Systems are the three different systems of measuring angles. Sexagesimal system is also known as English system and centesimal system is known as French system.

To convert the one system to the other system its very necessary to know the relation among the Sexagesimal system, Centesimal system and Circular system.

The relation between Sexagesimal, Centesimal and Circular systems are discussed below:

Since 90° = 1 right angle, hence, 180° = 2 right angles.

Again, 100g = 1 right angle; hence, 200g = 2 right angles.

And, πc = 2 right angles.

Therefore, 180° = 200g = πc.Let, D°, Gg and Rc be the sexagesimal, centesimal and circular measures respectively of a given angle.

Now, 90° = 1 right angle

Therefore, 1° = 1/90 right angle

Therefore, D° = D/90 right angle

Again, 100g = 1 right angle

Therefore, 1g = 1/100 right angle

Therefore, Gg = G/100 right angle.

And, 1c = 2/π right angle

Therefore, Rc = 2R/π right angle.

Therefore we have,

D/90 = G/100 = 2R/π

               or,

D/180 = G/200 = R/π

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