真题
1 . 风电项目对于调整能源结构和转变经济发展方式具有重要意义.某电力部门在某地安装了一批风力发电机,如图(1)某校实践活动小组对其中一架风力发电机的塔杆高度进行了测量,图(2)为测量示意图(点
,
,
,
均在同一平面内,
).已知斜坡
长为20米,斜坡
的坡角为
,在斜坡顶部
处测得风力发电机塔杆顶端
点的仰角为
,坡底与塔杆底的距离
米,求该风力发电机塔杆
的高度.
(结果精确到个位;参考数据:
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aee6e4e9350a2665df8597ff8045bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c83b688911f105cffe00d6d54eea13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(结果精确到个位;参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac980ce194582899d857b5f6edd431e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702e8d9602884d50948248734a1e1324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a0f8f5fabed2f1e761cd55660526c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
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名校
2 . 如图,一勘测人员从山脚B点出发,沿坡度为
的坡面
行至D点处时,他的垂直高度上升了15米;然后再从D点处沿坡角为
的坡面
,以20米/分钟的速度到达山顶A点时,用了10分钟.
(2)求山顶A点处的垂直高度
是多少米?(
,结果保留整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
(2)求山顶A点处的垂直高度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52881be613aa404e553da30d8987cfad.png)
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3 . 为打造旅游休闲城市,某村庄为吸引游客,沿绿道旁的母亲河边打造喷水景观(如图1).为保持绿道地面干燥,水柱呈抛物线状喷入母亲河中.图2是其截面图,已知绿道路面宽
米,河道坝高
米,坝面AB的坡比为
(其中
),当水柱离喷水口O处水平距离为2米时,离地平面距离的最大值为3米.
(1)求水柱所在抛物线的解析式;
(2)出于安全考虑,在河道的坝边A处安装护栏,若护栏高度为1.2米,判断水柱能否喷射到护栏上,说明理由;
(3)河中常年有水,但一年中河水离地平面的距离会随着天气的变化而变化,水柱落入水中能荡起美丽的水花,从美观角度考虑,水柱落水点要在水面上;
①河水离地平面
距离为多少时,刚好使水柱落在坝面截线
与水面截线的交点处?
②为保证水柱的落水点始终在水面上,决定安装可上下伸缩的喷水口,设坝中水面离地平面距离为h米,喷水口离地平面的最小高度m随着h的变化而变化,直接写出m与h的关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d257ee9c4cc6734d6133176abfc1404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bbf35fe2349c32441815e225ef129f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff3af2c91247039ef53ae46a88f0109.png)
(1)求水柱所在抛物线的解析式;
(2)出于安全考虑,在河道的坝边A处安装护栏,若护栏高度为1.2米,判断水柱能否喷射到护栏上,说明理由;
(3)河中常年有水,但一年中河水离地平面的距离会随着天气的变化而变化,水柱落入水中能荡起美丽的水花,从美观角度考虑,水柱落水点要在水面上;
①河水离地平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②为保证水柱的落水点始终在水面上,决定安装可上下伸缩的喷水口,设坝中水面离地平面距离为h米,喷水口离地平面的最小高度m随着h的变化而变化,直接写出m与h的关系式.
您最近一年使用:0次
4 . 如图,在一个建筑物两侧搭两个长度相同的滑梯(即
),设计要求左、右两边的滑梯
,
的坡度分别为
和
.测得
米,
米.
(2)试猜想两个滑梯
,
的位置关系,并证明;
(3)小亮(看成点)
从点
沿滑梯
下滑,请直接 写出他与
处距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da8fe8f5f8a3f17561d70652ad1172a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe7344afd6e0ef8760c57bfaad647b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b515965c22d2950b592c096c6e3bdfd4.png)
(2)试猜想两个滑梯
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)小亮(看成点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
7日内更新
|
47次组卷
|
3卷引用:2024年河北省张家口市九年级中考三模数学试题
5 . 如图,是一个山坡的纵向剖面图,坡面
的延长线交地面
于点B,点E恰好在
的中点处,
,坡面
的坡角为
,山坡顶点D与水平线
的距离,即
的长为
.
________;
_________;
(2)求
的长度;
(3)求
的长度.(结果保留根号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1212f222bed8b39156d13de8a35f40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048c5dbe93688bc276d5100bfbf82119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b5c0e0724cce5c25a88dca5e9220c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccb75185560eebab2a841cd2632a3be.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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6 . 某数学实践小组测量某古塔
,如图,
是一个斜坡,坡面
的坡度为:
,在斜坡点C处测得塔顶A处的仰角为
,古塔
与水平地面
垂直,测得
米,
米,求古塔
的高.(结果精确到
米.已知点A、B、C、D都在一个平面中,参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09824eebae0979a2b6b1fcc4d04bdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53e3cd4566cc35d715806d5fca506db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432cce1481829c4dfe2bd557f6e9aa4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d92accf6e50007ee4b73b16487f78a.png)
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名校
7 . “科技改变生活”,小王同学是一个摄影爱好者,入手了一个无人机用于航拍.在一次航拍时,小王在B处测得无人机A的仰角为
,登上斜坡
的C处测得无人机A的仰角为
.若斜坡
的坡比为
,C处的铅垂高度
为1.5米(点M,B,N在同一水平线上),求此时无人机的高度
.(结果精确到0.1米,参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7451b9d94e28503b8ac931632ff9dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9d5d7811052787a96c64e72bbc1559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9276f5c80582d75a9731f68947c5d08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a91fa163ba018df2dcf31e86f10180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c114c8734f0d064de64d8457655a980c.png)
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8 . 某大型购物中心为方便顾客地铁换乘,准备在底层至
层之间安装电梯,截面图如图所示,底层与
层平行,层高
为9米,A、B间的距离为5.2米,
.
(2)若采取中段平台设计(如图虚线所示),已知平台
,且
段和
段的坡度
,求平台
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b20a7e6f868962c97fc6d63e53199cf.png)
(2)若采取中段平台设计(如图虚线所示),已知平台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd721393a3d94cd3560678a50731792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862730f28c12750ebea0af5edcac5fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09824eebae0979a2b6b1fcc4d04bdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
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名校
9 . 位于海南省儋州市的东坡书院是全国重点文物保护单位,是苏轼谪居儋州时期的讲学场所.某校开展综合实践活动,小华借助一个斜坡测量书院内载酒亭的高度
,如图,坡长
米,坡角为
,在
处测得载酒亭顶端
的仰角为
,在
处测得载酒亭顶端
的仰角为
.(已知点
,
,
,
在同一平面内,
,
在同一水平线上)
______度;
______度;
(2)求点
到地面
的距离;
(3)求载酒亭的高度
(结果取整数).(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.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/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/8455657dde27aabe6adb7b188e031c11.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/386cda9f96731510d52ec18199e18286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802a939a9ab14a1a762a4275c9ec6899.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)求载酒亭的高度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed57cd3d54a8595cf9c3522b1048a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a110ab2e0c3f3e2a58ca71dd097d1a9c.png)
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10 . 如图,在坡顶
处的同一水平面上有一座网络信号塔
,数学兴趣小组的同学在斜坡底
处测得该塔的塔顶
的仰角为
,然后他们沿着坡度为
的斜坡
攀行了26米到达坡顶,在坡顶
处又测得该塔的塔顶
的仰角为
.
(1)坡顶
到地面
的距离;
(2)网络信号塔
的高度(结果精确到0.1米).(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f506e1c5584ae3c4d287c49f75a752dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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(1)坡顶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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(2)网络信号塔
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0e0ff475f32fa5dac263eacc92f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212f307d22e45797201804c95e08c504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3a4ad5d07fb718185561f40f39970d.png)
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