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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

Ravi
askIITians Faculty 69 Points
6 years ago
As angle needs to be formed between two lines, you can try doing this considering 2 arms at a time, which means that there are going to be 3 parts for this question. i.e. min-hr; hr-sec and min-sec.

So I’ll explain it for hr-min hand which is more practical and doable. So, firstly,
calculate the angular speed of hr hand and min hand. Now, assume a time being variable of the form m hrs and n minutes. So angle formed between the two arms would the difference of the two angles obtained by the product of angular speed and the timein terms of m:n.
0.5(60m+n)-6(n)=(+or-)90

Here, 0.5degrees/min=speed of hr hand
6 degrees/min=speed of min hand
time assumed m hrs and n minutes

Hence, we obtain a formula to calculate the time at which the clock’s 2 arms will make right angles.

0<m<13, put the values to get 2 values of minute hand(one for +90 and other for -90).

Overall, 24 such instances will take place in 12 hr lap.

Simlarily, it can be done for the other 2 parts(which is quite impractical as speed of minute hand is very high, so can be calculated for only a small duration)

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