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### Circumference of a Globe

```
Date: 1/27/96 at 12:31:19
From: PAUL H. OLDENBURG
Subject: Circumference of globe

Dear Dr. Math,

I need to get the formula to ascertain the circumference of a large
(15- to 20-foot) diameter globe hung 25 feet in the air. My guess is
to measure the width of the shadow and follow the formula (which I

Thank you,
Paul Oldenburg
```

```
Date: 7/29/96 at 13:21:25
From: Doctor Jerry
Subject: Re: Circumference of globe

If the shadow is produced by sunlight falling on the globe and we may
assume that the rays are parallel (since the sun is so far away this
is very nearly true), then draw a figure with a circle above a
horizontal line.  Draw in two rays, one just grazing the topside of
the globe and the  other the bottom side.  These rays will be
separated, since they are parallel, by the diameter D of the globe
(from which the circumference can be found).  Let the acute angle from
the floor towards the sun be called A.  With its base on the floor
there is a right triangle with hypotenuse w (width of the shadow)
and acute angle A opposite the leg of length D.

We note that sin A = d/w.

So, knowing A and w you can calculate d and, then, the circumference.

I'm not sure this answers the questions you asked.  Note that the
height of the globe doesn't matter.  This is a consequence of the
assumption that the rays of light are parallel.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

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