SOLUTION: what is the angle at the time 5:24

Question 410535: what is the angle at the time 5:24

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
each hour hand represents 1/12 of of a complete circle.

the number of degrees in a complete circle is 360 degrees.

each hour hand is therefore equal to 360 / 12 = 30

the 0 degree point is when the hour hand is on 12.

when the hour hand is on 1, the number of degrees from the 0 point is equal to 1 * 30 = 30.

when the hour hand is on 12, the number of degrees from the 0 point is equal to 12 I 30 = 360 degrees which is the same as 0 degrees because one complete revolution is equal to 360 degrees.

when the hour hand is on 5, the number of degrees from the 0 point is equal to
5 * 30 = 150 degrees.

since there are 60 minutes between hours, when the time is 5:24, the hour hand is on 5 + 24/60.

24/60 is the same as .4

the hour hand is therefore on 5.4.

5.4 * 30 = 162 degrees.

now to the minute hand.

there are 12 * 5 minute marks on the clock.

that's a total of 60 minute marks.

each minute is therefore equal to 360/60 = 6 degrees.

when the little hand is on the 24 (4 minutes past the 4 o'clock mark), the number of degrees from the 0 point is equal to 24 * 6 = 144 degrees.

the angle between the little hand the the big hand is equal to 162 - 144 = 18 degrees.

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