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I want to know what is the angle between minute and hours hands at $7:35$ P.M

I have no Idea. could any one tell me?

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    $\begingroup$ How could you have no idea? $\endgroup$ – user67258 Aug 30 '13 at 16:18
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In $60$ minutes the hour hand moves 30 degree so in 35 minutes it would have moved

$$\frac{30}{60} \times 35 $$ $$=17.5^\circ$$

Hour hand at $17.5^\circ$ from 7 . minute hand exactly points at 7 , so angle between minute hand and hour hand = $17.5^\circ$

I would point you to an online tool

clock angle calculator

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Hint: Measuring angles clockwise from straight up in degrees, at $7:00$ the minute hand is at $0^\circ$ and the hour hand is at $210^\circ$. What is the rate of motion of the hour hand in degrees/hour? What fraction of an hour is $35$ minutes? The minute hand will be at $210^\circ$

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$1$ hour for the hour hand = $5$ minutes for the minute hand = 30°.

The minute hand is obviously at $210°$.

The hour hand is between $210°$ and $240°$. Now, to get the exact amount between this two: $$ x:35 = 30°:60 $$ $$ x:35 = 1°/2 $$ $$ x = 35°/2 = 17.5° $$

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  • $\begingroup$ Yeah, I was counting angles from 3 hours (too used to trigonometry). $\endgroup$ – geodude Aug 30 '13 at 15:44
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Hint: Since 35 minutes have elapsed out of the 60 minutes in an hour, the hour hand will have moved $\frac{35}{60}$ of the angle between the 7 and the 8. Now, what is the angle between the 7 and the 8?

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The minute hand will have travelled $\frac{35}{60}\cdot 360$ degrees from "straight up."

The hour hand is a little trickier. Every hour it travels through $\frac{360}{12}=30$ degrees. So at $7:35$ it has travelled $\left(7+\frac{35}{60}\right)\cdot 30$ from straight up.

Calculate, subtract.

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  • $\begingroup$ Thank you, my calculator's caffeine supply was low. $\endgroup$ – André Nicolas Aug 30 '13 at 15:48
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assuming the hour hand moves "continuously over time" then the angle the hour hand from 12 o'clock is $2\pi(7+ \frac{35}{60})/12$ and the angle of the minute hand is $2\pi(35/60)$... so just find the difference.

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assuming:
h: 0-11 -> hour
m: 0-59 -> minute
s: 0-59 -> second
then

the always correct formula is:
A = 30 h - 11/2 m - 11/120 s
Angle = min {|A| , 360-|A|}

and in your case:
h = 7
m = 35
s = 0
=> A = 30*7 - 11/2 * 35 = 17.5
Angle = min {|17.5| , 360 - |17.5|} = min {17.5 , 342.5} = 17.5

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  • $\begingroup$ You should consider explaining a bit more in your answers. This is not enough for the OP or anyone new to the problem to understand. $\endgroup$ – Singhal Dec 7 '14 at 11:24

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