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Trigonometry and Pendulum Motion

One great way to measure vertical change of a pendulum using trigonometry (from Dr Math: http://mathforum.org/library/drmath/view/61280.html) 

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") = ------------

              l        ength 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