- #1
ador250
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a clock was set 10 am 20 minutes 30 second ? what will be the angle between hour & second hand ??
ans : 130.25° or 133° which one is correct? I'm confused
ans : 130.25° or 133° which one is correct? I'm confused
Angle Between Hour & Second Hand:130.25° or 133°?
- Thread starter ador250
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In summary, the clock was set 10 am 20 minutes 30 seconds and what will be the angle between hour & second hand?
- #2
Ryuzaki
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The line of reasoning should be as follows:-
It takes 12 hours for the hour hand to make a complete 360° rotation, i.e.
12 hours-------> 360°
==> 1 hour -------> 30°
==> 60 min -------> 30°
==> 1 min -------> 0.5°
==> 20.5 min -------> 10.25°
So, in a time period of 20.5 minutes, the hour hand would have traversed 10.25°.
Now, when the clock shows 10 A.M exactly, the hour hand has traversed 300° (since for each hour, the hour hand traverses 30°. So, after 10 hours exactly, it has traversed 300°). And in a further 20 minutes and 30 seconds, i.e. 20.5 minutes, it would have traversed 10.25° further, as we have just calculated above. So, the total angular distance traversed by the hour hand is (300+10.25)° = 310.25°.
Now, the second hand is at the exact position '6' in the clock (since it travels for a period of 30 seconds), and hence has traversed exactly half of the clock, thus traveling an angular distance of 180°.
Therefore, the angle between the hour hand and the second hand would be (310.25 - 180)° = 130.25°.
Hope that makes it clear!
It takes 12 hours for the hour hand to make a complete 360° rotation, i.e.
12 hours-------> 360°
==> 1 hour -------> 30°
==> 60 min -------> 30°
==> 1 min -------> 0.5°
==> 20.5 min -------> 10.25°
So, in a time period of 20.5 minutes, the hour hand would have traversed 10.25°.
Now, when the clock shows 10 A.M exactly, the hour hand has traversed 300° (since for each hour, the hour hand traverses 30°. So, after 10 hours exactly, it has traversed 300°). And in a further 20 minutes and 30 seconds, i.e. 20.5 minutes, it would have traversed 10.25° further, as we have just calculated above. So, the total angular distance traversed by the hour hand is (300+10.25)° = 310.25°.
Now, the second hand is at the exact position '6' in the clock (since it travels for a period of 30 seconds), and hence has traversed exactly half of the clock, thus traveling an angular distance of 180°.
Therefore, the angle between the hour hand and the second hand would be (310.25 - 180)° = 130.25°.
Hope that makes it clear!
- #3
jbriggs444
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The more interesting question is how the other answer was obtained.
Offhand, it looks like a factor of 12 got erroneously applied to the seconds correction.
Offhand, it looks like a factor of 12 got erroneously applied to the seconds correction.
- #4
Ryuzaki
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jbriggs444 said:
The best explanation I could come up with is, that the OP first figured that at exactly 10:20 A.M, the hour hand would have traversed 310°. Then, for the remaining 30 seconds, he mistakenly calculated the angular distance traversed by the minute hand, which turns out to be 3°, and then added it to the angular distance traversed by the hour hand, giving him the final value of the latter as 313°. And since the second hand has traversed 180°, he obtains (313 - 180)° = 133°, which is false.
- #5
jbriggs444
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Ryuzaki said:
Nice. That fits.
- #6
ador250
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got it man...thanks :)
1. What is the formula for calculating the angle between the hour and second hand?
The formula for calculating the angle between the hour and second hand is:
Angle = |(30 * H) - (5.5 * M)|
Where H is the current hour and M is the current minute. The absolute value is used to account for the possibility of the angle being greater than 180 degrees.
2. How do you convert the angle between the hour and second hand from degrees to minutes?
To convert the angle between the hour and second hand from degrees to minutes, you can use the formula:
Minutes = (Angle * 2) / 3
This will give you the number of minutes that have passed since the hour hand and second hand were aligned.
3. Why is the angle between the hour and second hand sometimes greater than 180 degrees?
The angle between the hour and second hand can be greater than 180 degrees when the hour hand is moving past the next hour mark and the second hand is close to the preceding minute mark. This happens because the hour hand moves slower than the second hand, causing the angle between them to increase.
4. How does the angle between the hour and second hand change throughout the day?
The angle between the hour and second hand changes throughout the day as the hour hand and second hand move continuously. The angle is constantly changing and can range from 0 degrees (when the hands are aligned) to 180 degrees (when the hands are directly opposite each other).
5. How can the angle between the hour and second hand be used to tell time?
The angle between the hour and second hand can be used to tell time by determining the number of minutes that have passed since the hour hand and second hand were aligned. This can be done by using the conversion formula mentioned in question 2. The result can then be added to the current hour to get the time in minutes. For example, if the angle is 130.25 degrees, then the time would be 2:10 minutes past the current hour.
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