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Circumference of a Globe

Date: 1/27/96 at 12:31:19
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 
need) to determine the circumference. Please help.

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
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Associated Topics:
High School Trigonometry

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