Find the degrees and radians the angle between the hour hand and the minute hand of a clock at half past three.

Answer

`75^@or(5pi)/12rad`

Explanation

The angle traced by the hour hand in `12 h =360^@`
Therefore, the angle traced by the hour hand in 3 h 30 min, i.e.,
`7/2h=(360/12xx7/2)^@=105^@`
The angle traced by the minute hand in 60 min
`=360^@`
The angle traced by the minute hand in 30 min
`(360/60xx30)^@=180^@`
Hence, required angle between the two hands
`180^@-105^@=75^@=(75xxpi/180)=(5pi)/12 " rad"`