Question

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 $x?$

$2.0$

$2.1$

$2.2$

$2.3$

$2.4$

Answer: E

Concepts:Pythagorean Theorem right triangle

Difficulty rating: 1140

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, $\begin{aligned} x^2+1^2 &= (5-x)^2 \\ &= x^2-10x+25, \end{aligned}$ so $10x=24$ and $x=2.4.$

Thus, the correct answer is E.

2009 AMC 10B Problem 10

Answer: E

Difficulty rating: 1140

Solution:

Problem 10 in Other Years