)阳光明媚的一天,数学兴趣小组的同学去操场上测量旗杆的高度,

)阳光明媚的一天,数学兴趣小组的同学去操场上测量旗杆的高度,他们带了以下测量工具:皮具、三角尺、标杆、小平面镜等.

首先,小明说:我们用皮尺和三角尺(含30角)来测量”.于是大家一起动手,测得小明与旗杆的距离AC15,小明的眼睛与地面的距离为1.6,如图9(甲)所示.

然后,小红和小强提出了自己的想法.

小红说:我用皮尺和标杆能测出旗杆的高度.”

小强说:我用皮尺和小平面镜也能测出旗杆的高度!

根据以上情景,解答下列问题:

1)利用图9(甲),请你帮助小明求出旗杆AB的高度(结果保留整数.参考数据:);

2)你认为小红和小强提出的方案可行吗?如果可行,请选择一中方案在图9(乙)中画出测量示意图,并简述测量步骤.

答案

解:(1)过点DDEAB于点E

RtBDE中,DE=AC=15m,∠BDE=30°

BE=DEtan30°≈15×058=870(m)

AB=BE+AE=870m+16m=103m10m

2)小红和小强提出的方案都是可行的

小红的方案:

利用皮尺和标杆:

1)测量旗杆的影长AG

2)测量标杆EF的长度

3)测量同一时刻标杆影长FH

小强的方案:

把小平面镜放在适当的位置(如图点P处),使得小强可以在镜中看到旗杆AB的顶端

步骤:

1)测出AP的长度

2)测出NP的长度

3)测出小强眼睛离地面的高度MN

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