Clock Hands

Date: 01/14/98 at 02:00:55
From: kim
Subject: Clock hands

The minute hand of a clock is 3 cm longer then the hour hand. If the 
distance between the tips of the hands at nine o'clock is 15 cm, how 
long is the minute hand?

Date: 01/15/98 at 09:22:16
From: Doctor Joe
Subject: Re: Clock hands

Dear Kim,

Let the length of the minute hand be x cm.
Then the length of the hour end hand is (x-3) cm.

When we look at the position of the hands at 9 o'clock, we see that 
the two hands are at right angles:

                                    12

                                     |
                                     |
                                     |
                                     |
                                     |
                      9      ________|


The next thing you should do is to find the distance between the tips 
at this position.  (Hint: use the famous Pythagoras Theorem.)

Then form a quadratic equation in x.

If you have any further difficulties solving this question, please 
feel free to ask again. I don't want to rob you of all the fun of 
solving this problem.

-Doctor Joe,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/