Question

Convert 70° 45'30" into centesimal measurement​

Answer 1

Answer:

Definition of systems of measuring angles:

(a) Sexagesimal System: In Sexagesimal System, an angle is measured in degrees, minutes and seconds.

A complete rotation describes 360°. In this system, a right angle is divided into 90 equal parts and each such part is called a Degree (1°); a degree is divided into 60 equal parts and each such part is called a Sexagesimal Minute (1’) and a minute is further sub-divided into 60 equal parts, each of which is called a Sexagesimal Second (1’’). In short,

1 right angle

1 degree (or 1°)

and 1 minute ( or 1’ )

= 90 degrees (or 90°)

= 60 minutes ( or 60’)

= 60 seconds ( or 60’’).

(b) Centesimal System: In Centesimal System, an angle is measured in grades, minutes and seconds. In this system, a right angle is divided into 100

equal parts and each such part is called a Grade (1g); again, a grade is divided into 100 equal parts and each such part is called a Centesimal Minute (1‵) ; and a minute is further sub-divided into 100 equal parts, each of which is called a Centesimal Second (1‶). In short,

1 right angle

1 grade ( or 1g)

and 1 minute (or 1‵) = 100 grades (or, 100g)

= 100 minutes (or, 100‵)

= 100 seconds ( or, 100‶).

Note: (i) Clearly, minute and second in sexagesimal and centesimal systems are different.

For example,

1 right angle = 90 × 60 = 5400 sexagesimal minutes = (5400)’

and 1 right angle = 100 × 100 = 10000 centesimàl minutes = (10000)‶

(ii) Since, 1 right angle = 90° = 100g

Therefore, 90° = 100g

or, 1° = (10/9) g and 1g = (9/10)°

The first relation is used to reduce an angle of sexagesimal system to centesimal system and the second is used to reduce an angle of centesimal system to sexagesimal system.

(c) Circular System: In this System, an angle is measured in radians. In higher mathematics angles are usually measured in circular system. In this system a radian is considered as the unit for the measurement of angles.

Definition of Radian: A radian is an angle subtended at the center of a circle by an arc whose length is equal to the radius.

Answer 2

Answer:

here it is better to convert to seconds rather than minutes.

but I'll do both .

1 degree = 60 minutes

70 degree = 4200 minutes

===> total ===> 4245 minutes and 30 seconds===> 4245' 30"

the above answer is the required one .

now if you need you can convert everything into seconds ===>( 4245 × 60)+30 ===>254730"

but the first one is. the standard answer..ok??