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

### 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

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

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