Clock Hands Perpendicular

Date: 10/15/2001 at 22:14:21
From: Carla Taylor
Subject: Math

What time of day is it when the hour hand is perpendicular to the 
minute hand and the minute hand points to the number 12?

Date: 10/16/2001 at 13:21:32
From: Doctor Sarah
Subject: Re: Math

Hi Carla - thanks for writing to Dr. Math.

Do you know what perpendicular means? Two lines that are perpendicular 
form a right angle of 90 degrees, or what looks like the corner of a 
square, when they meet.

So let's draw a picture, starting with the minute hand. We know that 
the minute hand is pointing to the number 12:

          12
    11     ^    1
           |
 10        |        2
           |
 9         o         3
            
   8               4         
      7         5 
           6


Now we'll draw an hour hand perpendicular to the minute hand:

          12
    11     ^    1
           |
 10        |        2
           |
 9         o------>  3   What time does this clock show?
            
   8               4         
      7         5 
           6



But wait! There's another way to draw the hour hand perpendicular to 
the minute hand...


          12
    11     ^    1
           |
 10        |        2
           |
 9  <------o         3   What time does this clock show?
            
   8               4         
      7         5 
           6

Does this help?

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/16/2001 at 12:11:56
From: Doctor Achilles
Subject: Re: Math

Hi Carla,

Thanks for writing to Dr. Math.

The minute hand points to 12 every hour on the hour. In other words, 
at 1:00, 2:00, 3:00, 4:00, etc., 12 is straight up, so your question 
is which number is perpendicular to 12. 

If you look at a clock, you'll see that 3 and 9 are both perpendicular 
to 12, so there are two times of day that work: 3:00 and 9:00.

Hope this helps. If you have other questions about this or other math 
topics, please write back.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/