# angle between minute and hours hands at $7:35$ P.M

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?

• How could you have no idea? – user67258 Aug 30 '13 at 16:18

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

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 $210^\circ$

$1$ 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: $$x:35 = 30°:60$$ $$x:35 = 1°/2$$ $$x = 35°/2 = 17.5°$$

• Yeah, I was counting angles from 3 hours (too used to trigonometry). – geodude Aug 30 '13 at 15:44

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?

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.

• Thank you, my calculator's caffeine supply was low. – André Nicolas Aug 30 '13 at 15:48

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.

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|}