Question

If D, G and R denote respectively the number of degrees, grades and radians in an angle, the 

विकल्प

• \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
  
  
• \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
  
  
• \[\frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi}\]
  
  
• \[\frac{D}{90} = \frac{G}{100} = \frac{R}{2\pi}\]

Answer 1

\[\frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi}\]

Explanation:

Let θ be the angle which is measure in degree, radian and grade.

We know that 90° = 1 right angle

⇒ 1° = `1/90` right angle

⇒ D° = `"D"/90` right angle

⇒ `theta = "D"/90` right angle    ...(1)

Also we know that, π radians = 2 right angles

⇒ 1^C = `2/pi` right angle

⇒ R = `2/pi xx` R right angle 

⇒ `theta = 2/pi xx` R right angle   ...(2)

Also we know that, 100 grades = 1 right angle 

⇒ 1 grade = `1/100` right angle

⇒ G grade = `"G"/100` right angle

⇒ `theta = "G"/100` right angles   ...(3)

From (1), (2) and (3)

∴ `"D"/90 = "2R"/pi = "G"/100`