Associated Topics || Dr. Math Home || Search Dr. Math

### 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.

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Puzzles

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search