Difference between revisions of "2009 AMC 10B Problems/Problem 10"
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Revision as of 11:53, 4 July 2013
Problem
A flagpole is originally 
meters tall. A hurricane snaps the flagpole at a point 
meters above the ground so that the upper part, still attached to the stump, touches the ground 
meter away from the base. What is ?
Solution
The broken flagpole forms a right triangle with legs and , and hypotenuse 
. The Pythagorean theorem now states that 
, hence 
, and 
.
(Note that the resulting triangle is the well-known 
right triangle, scaled by 
.)
See Also
| 2009 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
