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 $x$?
$\text{(A) } 2.0 \qquad \text{(B) } 2.1 \qquad \text{(C) } 2.2 \qquad \text{(D) } 2.3 \qquad \text{(E) } 2.4$
The broken flagpole forms a right triangle with legs $1$ and $x$, and hypotenuse $5-x$. The [Pythagorean theorem](https://artofproblemsolving.com/wiki/index.php/Pythagorean_theorem) now states that $1^2 + x^2 = (5-x)^2$, hence $10x = 24$, and $x=\boxed{2.4}$.
(Note that the resulting triangle is the well-known $5-12-13$ right triangle, scaled by $1/5$.)