2009 AMC 10B Problem 10

Below is the professionally curated solution for Problem 10 of the 2009 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 10B solutions, or check the answer key.

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Concepts:Pythagorean Theorem right triangle

Difficulty rating: 1140

10.

A flagpole is originally $5$ meters tall. A hurricane snaps the flagpole at a point $x$ meters above the ground so that the upper part, still attached to the stump, touches the ground $1$ meter away from the base. What is $x?$

$2.0$

$2.1$

$2.2$

$2.3$

$2.4$

Solution:

The standing stump has height $x,$ and the snapped piece of length $5-x$ is the hypotenuse of a right triangle with legs $x$ and $1.$ By the Pythagorean Theorem, $x^2+1^2=(5-x)^2=x^2-10x+25,$ so $10x=24$ and $x=2.4.$

Thus, the correct answer is E.

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