Question

At whay time btween 2pm and 3pm the angle between minute hand and hour hand is 120

Answer 1

Answer:

At 2:10:49 PM the angle between minute hand and hour hand is 120

Step-by-step explanation:

Angle A in degree is given by the formula

A= |30H-5.5M|

H= hours

and M= minute

120= |30×2-5.5M|

120= 60-5.5M

60= 5.5M

⇒M= 60/5.5

M= 10.8181 minutes

M= 10 minutes and 49 seconds.

So, At 2:10:49 PM the angle between minute hand and hour hand is 120

Answer 2

Answer:

At 2:32:43.6 will the hands of a clock form an angle of 120 degrees.

Step-by-step explanation:

At 2:32:43.6 will the hands of a clock form an angle of 120 degrees.

[5.5m = 120+60 = 180, or m = 180/5.5 = 32.72]

Formula:-

angle = (30*H) - (11/2 * M ), where H represents the hour hand and M represents the minute hand.

In this case, H is 3 and M is 50, thus using the formula we get

Angle = (30*3)- (11/2*50)= -185 degree.

In the case of clock problems, we consider (+) to be clockwise and (-) to be anticlockwise.

Steps for finding the formula

Movement of hour hand = (30*H)

In 1 min scenario:-

The angle between Minute hand goes

= 360/60= 6 degree.

The angle between Hour hand goes = 30/60 = 1/2 degree.

So Relative distance between a minute and an hour's hand

= (6–1/2) *M= 11/2*M.

Thus we have the formula as the angle between two hands of a clock as:-

(30*H) -(11/2*M).