1 . 杭州世纪中心是杭州最高楼,同时是浙江省最高的双子塔楼,建筑高度310米,以杭州拼音首字母“
”为外形蓝本,被称为杭州之门,双塔的设计像一对翅膀,结合了杭州文化的城市之形,拱桥之意。某位高中生想运用所学知识测量验证一下高度,通过查阅资料获取了两种测量方案.
方案一(“两次测角法”):如图一,在双子塔附近广场上的
点测得双子塔顶部的仰角为
,正对双子塔前进了
米后,到达
点,在
点测得双子塔顶部的仰角为
,然后计算出双子塔的高度.
米;②正对双子塔,将镜子后移
米,重复①中的操作,测量出人与镜子的距离为
米.然后计算出双子塔的高度.
实际操作中,方案一测量数据为
米,
,测得双子塔高度为
;方案二测量数据为
米,
米,
米,测得双子塔高度为
;假设测量者的“眼高
”都为1.6米.
(1)试用
表示出
;
(2)计算
的实际测量值(结果取整,参考数据:
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c4fd6998a8748375793cd1674f7417.png)
方案一(“两次测角法”):如图一,在双子塔附近广场上的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
实际操作中,方案一测量数据为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a110bb6e761a161260c92dea2121d2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048e023d71c00d7d79c08ab66ce0fb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86163e76653de1f383788b741fb64a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbb5c16657599a529e542a74eac4805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6da0a29001235bb32594352d268d229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbebc3df0e44aaf7c04feebcf5d70dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1fae01485740cbb48b5c79f1185b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20052748de237fef46f62671b4fd7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86163e76653de1f383788b741fb64a8b.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45eb4c210d02b62d0d45cbf83a052dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1766ff3477d0f112b2f00c4f1bbf0494.png)
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2 . 如图,一座山其高
为
,一辆汽车在一条水平的公路上沿直线从
往
匀速行驶,在
处测得山顶
的仰角为
,经过
后汽车到达
处,这时测得山顶
的仰角为
,且
.
(2)若汽车从
往
行驶5秒时到达
处,求此时山顶
与汽车的距离
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e55c43b32c647e9d23bfcfc9920458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9f5b0481869bd5befe1d112797b87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
(2)若汽车从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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2021-07-30更新
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601次组卷
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5卷引用:江苏省连云港市海州高级中学2023-2024学年高一下学期期中学情调查考试数学试题