at what time between 7 and 8 o clock the hands of the clock are at right angle ?
Answers
Given : hands of a clock at right angles between 7 am and 8 am
To Find : Time
Solution:
At what time are the hands of a clock at right angles between 7 am and 8 am
at 7 AM the angle between minute and hour clock are 210°
if Minute hand moves (120 + x)° then Hour hand should move x° to have angle between them 90°
or Minute hand moves (300 + x)° then Hour hand should move x° to have angle between them 90°
for every 360° minute hand hour hand moves 30°
=> for every 1° minute hand hour hand moves 1/12°
case 1 : Minute hand moves (120 + x)° then Hour hand should move x° to have angle between them 90°
(120 + x)°/12 = x
=> 10 + x/12 = x
=> 11x/12 = 10
=> x= 12 * 10 /11
=> x = 120/11
360° minute hand = 60 minutes
Hence 6° minute hand = 1 minute
=> Time = (120 + 120/11) /6 = ( 20 + 20/11) = 20(12/11) = 21 minute 49 sec
7 past 21 9/11 minutes
7 past 21 minute 49 sec
case 2 : Minute hand moves (300 + x)° then Hour hand should move x° to have angle between them 90°
(300 + x)°/12 = x
=> 25 + x/12 = x
=> 11x/12 = 25
=> x= 12 * 25 /11
=> x = 300/11
360° minute hand = 60 minutes
Hence 6° minute hand = 1 minute
=> Time = (300 + 300/11) /6 = ( 50 + 50/11) = 50(12/11) = 54 minute 32 sec
7 past 54 6/11 minute
7 past 54 minute 32 sec
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: Required Answer
➝ Given
at what time between 7 and 8 o clock
➝ Find
clock are at right angle ?
➝ Solution
➝ When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min.
➝ Ha - Hm = 0.5 (60 × h - 11 × M)
➝ Ha - Hm = 90 °
➝ H = 7
➝ 90 = ( 60× 7- 11 × M )
M = 21.8. min 7 hands
hence 21.8 min will show right angle