A wall clock shows the time as 12hr.15mts. Then what will be the angle between the two hands of the clock?

6 Answers

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lynn30k | High School Teacher | (Level 1) Educator

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lit24 is the closest to being correct. If the hour hand did NOT move at all until one o'clock, the answer would be 90 degrees. However, the hour hand also moves continuously. You can calculate the exact angle: the minute hand is at the 3, when it is 15 minutes past. The hour hand will be 1/4 of the way between 12 and 1.  1/4 of those 5 minutes will be 1 and 1/4 "minutes" after the 12. Each "minute" on the clock corresponds to 6 degrees of the way around the circle of the clock, if you consider the clock as 360 degrees. Therefore, 1 and 1/4 minutes is equal to 7 1/2 degrees. Subtract that from 90, and you get 82 1/2 degrees.

Answer: 82.5 degrees.

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neela | High School Teacher | (Level 3) Valedictorian

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To calculate the angle between the hour angle and the minute angle when the time is 12hrs 15 minutes.

This is a time and motion problem.

Let us take 12 o'clock as reference point, when both hour and minute handle make zero angle. The angular speed of the minute handle is 360 degree/60 minute =6 degree per minute and that of the hour handle is 360 degree/12 hour = 360deg/(12*60) minute = 0.5 dgree minute.

So every minute, the minute handle has  the relative angular speed  of (6-0.5) degree with reference to the hour handle.

Therefore, the relative angular motion of the minute handle with respect to the hour handle after 15 minutes past 12 o'clock is (6-0.5)*15 =  82.5 degrees. In other words, the angle between the hour handle and minute handle at 12 hour 15 minutes is 82.5 degrees or 82 degree 30 minutes.

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shoshana613 | Elementary School Teacher | eNotes Newbie

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Draw a clock face on a sheet of paper & place the hour hand (small) on the 12 and the minute hand on the 3 to show 12:15 (use a ruler or straight edge for precision).  Use a protractor to determine how many degress the 2 hands create. 

Be sure to remember that when we start adding minutes to the hour, the hour hand begins to slowly creep to the right.  Look at the clock on the wall, where is the hour hand?  Is it directly over the 12?  If so, it is a 90 degree or right angle.  However, if the hour hand is not directly over the 12, but is instead beginning to move clockwise, then it will be smaller than 90 degrees.  Therefore it will be an acute angle (acute angle is an angle that is less than 90 degrees). 

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lit24 | College Teacher | (Level 3) Valedictorian

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At 12 hours 15 minutes the hour hand will be at 12 and the minute hand will be at 3. Three into 5 will be equal to 15 minutes.

The angle will be 90 degrees or a right angle.

However, in many clocks the hour hand will not point exactly to 12, it may point to a minute or two after 12.  In which case the exact angle formed may be 88 or 89 degrees.

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mkcapen1 | Middle School Teacher | (Level 3) Valedictorian

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A clock is set up in 15 minute increments.  Each set of 15 minutes is a 90 degree angle.  A 90 degree angle is also called a right angle.  To recognize a right angle easily just look at a corner on a rectangle picture frame.  A well aligned frame rectangle frame will always have four 90 degree angles.  A clock also has a specific 90 degree angle if you start with the hour hand on the 12 and the minute hand on 15 minutes. 

Angles can be measured using a protractor.  If the protractor has the flat end at the center point aligned with the 12 and you go over to the 15.  The protractor will display 90 degrees.