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Question
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
Options
- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
- \[\frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi}\]
- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{2\pi}\]
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Solution
\[\frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi}\]
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
⇒ 1C = `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`
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