Question

the angle between the hour and minute hand of a clock at 10:10 is

Answer 1

At 10' o'clock:
The hour hand is at '10'(dial):
Angle between each dial = 30 degree
Hour hand angle at 10 = 30*10 = 300 degree
In 1 minute, minute hand moves 6 degree
In 10 mins, minute hand moves: 6*10 = 60 degree
In 1 min, hour hand moves: 0.5 degree
In 10 mins, hour hand moves: 10*0.5 = 5 degree
Total hour hand angle = 305 degree
Minute hand angle = 60 degree
Angle between hour hand and minute hand = 360- (305-60) = 360- 245 = 115 degrees.

Alternatively:
Formula:
11/2 * M - 30* H
11/2 * 10 - 30*10 = 55 - 300 = -245 = 245(since angle cant be negative)
Now, our required angle = 360 - 245 = 115

[N.B: why did we subtract ans from 360. Just imagine the clock : 10.10 means 'hour hand' is at 10 and 'minute hand' is at dial '2'. We have to find the angle between it(dial 10 and dial 2). The initial angle(245) is the region outside 10.10 i.e, the region from dial '2' to dial '10'. ]

Hope it helps.

Answer 2

In 60 mins hour hand advances 30 deg

In 10 mins hour hand advances = 10 *30 /60 =5 deg past 10

Min hand at 2 & hour hand is 5 deg towards 11

Angle between 10 & 2 ‘o’clock =4 *30 =120°

Answer angle between H &M hands is= 120 -5 = 115°

Answer angle between H &M hands is 115° degrees

Check with formula = | 30*H -11/2* M |

= |30 *10 – 11/2 *10 | = |300 -55 | =245°

But this angle is Reflex angle other angle is =360 -245 =115°

Answer :At 10 .10 hrs angle between H &M hands is 115 °