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Diameter of Flying Saucer


Date: 5/27/96 at 10:57:19
From: Anonymous
Subject: Diameters of Flying Saucers

Dear Dr. Math,  I need some help on a landscaping project...	

We are constructing an oval racetrack in Atlanta, and while 
excavating for the project, we ran across a large circular object 
buried in the ground edgewise.  The portion that we have uncovered so
far measures 10 meters high by 30 meters across.  We have not dug down 
far enough to get a measurement on the diameter of this saucer-like 
object. But we need to know the diameter so that we can tell how far 
down we have to dig to get it out of the ground.  We don't want to 
spend too much time with this thing.  It is radioactive... Thanks!   


Date: 5/27/96 at 21:11:2
From: Doctor Ken
Subject: Re: Diameters of Flying Saucers

Hello!

The first thing you need to do is hire someone else with a yellow 
plastic suit to do your digging for you - no telling how your children 
will look with all that radioactivity leaking around.

So let's assume this flying saucer is indeed saucer-shaped (several of 
the flying saucers I've unearthed have looked like they were going to 
be saucer-shaped at first, but sometimes when I dug up the whole thing  
there was actually a big nose cone sticking directly downward, like 
the craft took a nose dive into the ground. I guess they haven't 
figured out how to land on our planet yet - perhaps their planet is 
softer!). I've made a picture of the saucer, and you can see it on the 
web at: 

      

With the parts labeled as I have them in my picture, you've measured 
the length of AC (it's half of 30, which is 15) and BC (which is 10).  
And you want to figure out the radius of the circle.  Well, notice 
that DA and DB are both radii, so they have the same length.  You can 
call that length R.  

Now look at the green triangle, triangle ACD. It's a right triangle, 
and the top leg has length 15. The hypotenuse has length R, and the 
other leg has length R-10. Can you use the Pythagorean Theorem to 
figure out R?  

Good luck!  And if you find any non-Earth creatures inside, tell 
them Doctor Ken says howdy.

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Triangles and Other Polygons

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