An angle is defined as the space included between two intersecting lines. The angle is usually measures in degrees.There are multiple systems for measuring angles, other than basic degrees. They are British, French, and Circular.
British System or Sexagesimal Measure:
In this system, each right angle is divided into 90 equal parts where each part is called a degree. Each degree is divided into 60 equal parts where each part is called a minute. Each minute is divided again into 60 equal parts where each part is called a second.
So,
1 right angle = 90 degrees (900)
10 = 60 minutes (60’)
1’ = 60 seconds (60’’)
This results in 90 degrees (900) being equal to 3600 seconds (3600”)
French System or Centesimal System:
In this system, each right angle is divided into 100 equal parts where each part is called a Grade. Each grade is then divided into 100 equal parts where each part is called a minute. Last, each minute is divided into 100 equal parts where each part is called a second.
So,
1 right angle = 100 grades (100g)
1g = 100 minutes (100’)
1’ = 100 seconds (100’’)
Circular System or Radian Measure:
In this system, the angle is measured in terms of radians where radian is defined as the angle subtended at the centre of the circle by an arc whose length is same as the radius of the circle and one radian is denoted by 1c.
Note:
2 right angles = 1800 = 200g = πc.
Converting Between Systems
Example 1: Express the Sexagesimal measure 300 as radian measure.
Solution:
We know that 1800 = πc
Þ 10 =
300 = 30 * π/180 = π/6
Example 2: Express the radian measure 5π/2 as Centesimal measure.
Solution:
We know that 200g = πc.
5π/2 = 5/2 * 200g = 500g.
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