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

### 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
ground.

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
pole.

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!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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