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Write the Different Ways of Measuring Angles The custom of measuring angles using degrees, with displaystyle{360}^{circ} in a circle, dates back to th

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asked 2020-11-08
Write the Different Ways of Measuring Angles The custom of measuring angles using degrees, with \(\displaystyle{360}^{\circ}\) in a circle, dates back to the ancient
Babylonians, who used a number system based on groups of 60. Another system of measuring angles divides the circle into 400 units, called grads. In this system a right angle is 100 grad, so this fits in with our base 10 number system.
Write a short essay comparing the advantages and disadvantages of these two systems and the radian system of measuring angles. Which system do you prefer?
Why?

Answers (1)

2020-11-09

There are three systems for the measurements of angles. That is,
(1) Sexagesimal system (unit is degree)
(2) Centesimal system (unit is grade)
(3) Radian or circular measure (unit is radian)
The comparisons between three systems are as follows:
Sexagesimal system: In this system, one right angle is equal to the 90 degrees (1 right angle \(\displaystyle={90}\) degrees), one degree is equal to 60 minutes (\(\displaystyle{1}^{\circ}={60}\) minutes) and one minute is equal to the 60 seconds (\(\displaystyle{1} \ minute={60}\ seconds\)).
Centesimal system: In this system, one right angle is equal to the 100 grades, one grade is equal to 100 minutes and one minute is equal to the 100.
Radian system! In this system, one right angle is equal to the 90 degrees (\(\displaystyle{1}\text{right angle}={90} \ degrees\)), one degree is equal to \(\displaystyle\frac{\pi}{{18}}0\), radians and one minute is equal to the 60 seconds (\(\displaystyle{1} \ minute={60}\ seconds\)).
\(\displaystyle\pi\text{radian}={180}^{\circ}={200}^{g}\)
The circular system or radian system is more preferable, because it gives the equivalence relation between other two systems.

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