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how many right angles are formed by a clock having hour,minute and second hands ?plese explain

how many right angles are formed by a clock having hour,minute and second hands ?plese explain

Grade:10

1 Answers

Malavika Rajesh
27 Points
9 years ago
We start at 12 midnight. The hands are together. For subsequent 90 degree angles to occur, the minute hand must "overtake" the hour hand by
90 degrees, then 270 degrees, then 360 + 90 degrees, then 360 + 270 degrees, then 360 + 360 +90 degrees.. and so on.
This can be re-expressed as: (1)90, 3(90), 5(90), 7(90), 9(90), 11(90)... n(90).
The number of minutes this takes to happen can be expressed as (1)90/5.5, 3(90)/5.5, 5(90)/5.5, 7(90)/5.5, 9(90)/5.5, 11(90)/5.5... n(90)/5.5.

In one day, there are 24 hr * 60 mins = 1440mins
To find the maximum value of n,
n(90)/5.5 = 1440
n = 88

but as seen from above, n must be an odd number (by pattern recognition and logic)
hence n must be the next smallest odd number (87)
counting 1,3,5,7,9,11......87, we see that the number of terms = (87-1)/2 +1 = 44.

In other words, the minute hand "overtakes" the hour hand on 44 occasions in 24 hours in order to give a 90 degree angle.
Therefore the answer to your question is 44.

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