Question

Find the angle between the hour-hand and the minute-hand in circular measure at half past 4
A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(6)`
D. None of these

Answer 1

Correct Answer - B
Angle traced by the hour hand in 12 hours = `360^(@)`
Angle traced by it in 4 hr 30 min `(4h+(30)/(60)hr)=(9)/(2)` hr
`=(9)/(2)xx(360)/(2)=135^(@)`
Angle traced by minute hand is `60^(@)` min = `360^(@)`
Angle traced by it in 30 min = `(30)/(60)xx360=180^(@)`
Required Angle `= 180^(@)-135^(@)=45^(@)implies45xx(pi)/(100)=(pi)/(4)` radian