AMC10 2004 B

AMC10 2004 B · Q8

AMC10 2004 B · Q8. It mainly tests Pythagorean theorem, Coordinate geometry.

Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. Which of the following is closest to the number of miles between downtown St. Paul and downtown Minneapolis?

明尼阿波利斯-圣保罗国际机场位于圣保罗市中心西南方 8 英里，明尼阿波利斯市中心东南方 10 英里。圣保罗市中心与明尼阿波利斯市中心之间的英里数最接近下列哪一个？

(A) 13 13

(B) 14 14

(D) 16 16

(E) 17 17

Answer

Correct choice: (A)

正确答案：（A）

Solution

Let downtown St. Paul, downtown Minneapolis, and the airport be located at S, M, and A, respectively. Then $\triangle MAS$ has a right angle at A, so by the Pythagorean Theorem, $MS = \sqrt{10^2 + 8^2} = \sqrt{164} \approx \sqrt{169} = 13$.

设圣保罗市中心、明尼阿波利斯市中心和机场分别位于 S、M 和 A。那么 $\triangle MAS$ 在 A 处有直角，因此由勾股定理，$MS = \sqrt{10^2 + 8^2} = \sqrt{164} \approx \sqrt{169} = 13$。

Topics