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Pendulum Altitude

Date: 09/26/2002 at 06:43:45
From: Relle
Subject: Trigonometry

This question is related to Trigonometry.

A pendulum 45cm long swings through a vertical angle of 30 degrees. 
Find the distance of the altitude through which the pendulum bob 
rises. (Answer: 1.533cm)

I have problems drawing (visualising) this picture, and am thus unable 
to solve this problem. Maybe if you could try to include a picture 
I'll be able to understand the answer better. Thanks.


Date: 09/26/2002 at 09:17:52
From: Doctor Ian
Subject: Re: Trigonometry

Hi Relle,

Here is a diagram of the situation:

       A                   
      /|\
     / | \               AP = AP' = AP"
    /  |  \
   /   |   \
  P'   |    P"
       P

It's not clear which of the following is the case:

  1) angle P'AP" = 30 degrees

  2) angle PAP"  = 30 degrees

I'll leave that for you to work out with your teacher. In either case, 
it's angle PAP" that you're interested in. Let's look more closely at 
that:

       A                   
       |\
       | \
       |  \
       |   \
       |    \              AC is vertical
       |     \             CP" is horizontal
       |      \            therefore angle ACP" = 90 degrees
       C.......P"          
       |        
       P

Now, note that

              length of AC
  cos(PAP") = ------------
              length of AP"

Can you take it from here? If you're having trouble following what I 
did, you might want to take a look at 

  Trigonometry in a Nutshell
  http://mathforum.org/library/drmath/view/53942.html 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Trigonometry

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