What is the measure of the angle `114^(@)` 35 ' 30" in radian ?

Options

A. 1 rad
B. 2 rad
C. 3rad
D. 4rad

Answer

B

Explanation

From relation between minute 6 seconds measure : 60 " = I '
`rArr30=(1)/(2)`'
`rArr35'30=(35+(1)/(2))=((71)/(2))`
Also , `60'=1^(@)`
`therefore1'=((1)/(60))@`
`rArr((17)/(2))=((71)/(2)xx(1)/(60))^(@)=((71)/(120))^(@)`
`therefore114^(@)35'30=(114+(71)/(120))^(@)=((13751)/(120))^(@)`
We know that , `2pi` rad = `360^(@)`
`rArr1^(@)=(2pi)/(360)`rad
`rArr((13751)/(120))^(@)=(2pi)/(360^(@))xx(13751)/(120)`rad
`=(2xx22xx13751)/(7xx360xx120)`rad = 2 .0008069 rad
`rArr114^(@)35'30=2`rad (approx.)