Question

Which angle will be formed at
i) 6:00
ii)5:00​

Answer 1

At 5:00, the hands are 150 degrees apart and the gap is closing every minute. Since the minutes hand sweeps 6 degrees per minute, and the hours hand sweeps 0.5 degrees per minute, the hands will be at a right angle after (150-90)/(6-0.5) = 60/5.5 = 10 min 54 & 6/11 sec. So the hands will be at a right angle at 5:10:54 + 6/11 sec.

However, the minutes hand will eventually sweep past the hours hand, and will eventually be 90 degrees past. This will happen after (150+90)/(6-0.5) = 240/5.5 = 43 min 38 & 2/11 sec. So the hands will also be at a right angle at 5:43:38 + 2/11 sec.

OR

At m minutes past 5, the hour hand is at 150 + 0.5m degrees, and the minute hand at 6m degrees.

The problem requires 150 + 0.5m ±90 = 6m or

5.5m = 60, or m = 10.9090… minutes.

and 5.5m = 240 or m = 43.6363…. minutes