Broken Flag PoleDate: 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/ |
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