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Broken Flag Pole

Date: 9/11/96 at 17:49:59
From: Stuart Lightfoot
Subject: Broken Flag Pole

Dr. Math,

I can't get started.  Please work it out for me and send equations.

A 90 ft high flag pole sits atop and in the corner of a 10 ft high, 10 
ft wide building. Hence, the tip of the flag pole is 100 ft
above ground.

The flag pole breaks at a point above the building roof so that an 
edge of the pole touches the building edge and the tip is touching the 

How far above the building did the pole snap?

Date: 9/18/96 at 11:18:15
From: Doctor Jerry
Subject: Re: Broken Flag Pole

Look at the building from the side, so that it is a 10 by 10 square, 
and draw from the upper left corner of the square the stub of the 

Next draw from the top of the stub a line just grazing the corner of 
the square and continuing on to the ground. Let the length of the stub 
be w.  Then the rest of the pole (which stretches from the top of the 
stub, past the corner of the building, and continuing on to the 
ground) is 90-w.

Here's a hint on how to get started. Let z be the horizontal length 
from the base of the building to the tip of the pole resting on the 
ground. From similar triangles, z= 100/w. Now use the Pythagorean 
Theorem on the biggest right triangle.  The result, after multiplying 
by w^2, will be a third degree equation. I think two of the roots are 
of interest.

A very nice problem!

-Doctor Jerry,  The Math Forum
 Check out our web site!   
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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