Question

一根旗杆原本高 $5$ 米。飓风使旗杆在离地 $x$ 米处折断，折断的上半部分仍连在残桩上，并触地于离底座 $1$ 米处。求 $x$ 的值。

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 $x?$

$2.0$

$2.1$

$2.2$

$2.3$

$2.4$

答案：E

知识点：勾股定理直角三角形

难度评级：1140

解答：

竖直残桩高为 $x$ ，长度为 $5-x$ 的折断部分是直角三角形的斜边，两条直角边为 $x$ 和 $1$ 。由勾股定理，所以 $10x=24$ ，从而 $x=2.4$ 。 $\begin{aligned} x^2+1^2 &= (5-x)^2 \\ &= x^2-10x+25, \end{aligned}$

所以正确答案是 E。

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 第 10 题

答案：E

难度评级：1140

解答：

其他年份的第 10 题