At what time between 10 O' clock & 11 O' clock are the two hands of clock symmetric with respect to the vertical line: A) 10h 9m 14s      B) 10h 9m 22s           C) 10h 9m...

At what time between 10 O' clock & 11 O' clock are the two hands of clock symmetric with respect to the vertical line: A) 10h 9m 14s      B) 10h 9m 22s           C) 10h 9m 50s        D) NONE

Expert Answers
justaguide eNotes educator| Certified Educator

The angle between the minute hand and the 12 O' clock line is given by `theta_M = 6*M` where M is the minutes that have passed.

The angle between the hour hand and the 12 O' clock line is given by `theta_H = (1/2)*(60H + M)`

For the given times it has to be determined when the two angles are the same. It has to be kept in mind that the two hands are on opposite sides of the 12 O' clock line.

At 10:9:14

`theta_M = 6*(9+14/60) = 55.4`

`theta_H = (1/2)(60*10+9+14/60) = 304.61` . As this line is on the other side, the angle is 55.38 `~~ 55.4`

At 10:9:22

`theta_M = 6(9+22/60) = 56.2`

`theta_H = (1/2)*(60*10 + 9 +22/60) = 304.68`

At 10:9:50

`theta_M = 6(9+50/60) = 59`

`theta_H = (1/2)*(60*10+9+50/60) = 304.91`

The time at which the two hands are symmetrical to the 12 O' clock mark is 10:9:14