Question

find in radian, the angle between the hour hand and minute hand of a clock at 2:25AM

Answer 1

An hour hand rotates 360⁰ in 12 hrs ,this means 30⁰ in 1 hr and 0.5⁰ in 1 minute.
A minute hand rotates through 360⁰ in 60 min or 6⁰ in 1 minute.

Now given time is 2:25 a.m.
At 2 '0' clock, angle subtended by hour hand from 12 'O' clock position is = 30⁰ +30⁰ =60⁰
At 2:25, that means after 25 min hour hand will move ahead by = 0.5⁰x25=12.5⁰
Total angle subtended by hour hand at 2:25=60⁰+12.5⁰=72.5⁰

At 2:25, angle subtended by minute hand from ​12 'O' clock position is = 6⁰x25=150⁰

Now the angle between hour hand and minute hand at 2:25 a.m. = 150⁰-72.5⁰=77.5⁰ (Angle measurement remains same for a.m and p.m.)