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人教版九年级下第二十八章《锐角三角函数》单元检测题含答案

《锐角三角函数》单元检测题

一、选择题（每小题只有一个正确答案）

1．sin30°的值等于（）

A. 12

2．已知∠A 为锐角，且sin A ，那么∠A 等于（） A. 15° B. 30° C. 45° D. 60° 3．在Rt ABC ?中， 90C ∠=?， 1cos 2B =

，则sin A 的值为（）

A. 12

4．在△ABC 中，若|cosA －12

|＋(1－tanB)2＝0，则∠C 的度数是( ) A. 45° B. 60° C. 75° D. 105°

5．如图所示，平地上一棵树高为6米，两次观察地面上的影子，第一次是当阳光与地面成60 时，第二次是阳光与地面成30 时，第二次观察到的影子比第一次长（）

A. 3

D. 3-

6．如图，在Rt △ABC 中，∠ACB=90°，CD⊥AB，垂足为D ，AB=c ，∠A=α，则CD 长为（）

A. c?sin 2α

B. c?cos 2α

C. c?sinα?tanα

D. c?sinα?cosα

7．根据所给条件解直角三角形，结果不能确定的是( )

①已知一直角边及其对角；②已知两锐角；③已知斜边和一锐角；④已知一直角边和一斜边；⑤已知直角边和一锐角．

A. ②③

B. ②④

C. 只有②

D. ②④⑤

8．如图，为安全起见，萌萌拟加长滑梯，将其倾斜角由45°降至30°．已知滑梯AB 的长为3m ，点D 、B 、C 在同一水平地面上，那么加长后的滑梯AD 的长是（）

B. C. D.

9．临沂高铁即将开通，这将极大方便市民的出行．如图，在距离铁轨200米处的B 处，观察由东向西的动车，当动车车头在A 处时，恰好位于B 处的北偏东60°方向上，10秒钟后，动车车头到达C 处，恰好位于B 处西北方向上，则这时段动车的平均速度是（）米/秒.

A. )201

B. )

201- C. 200 D. 300 10．如图，放置的1OAB ， 112B A B ， 223B A B ，…都是边长为2的等边三角形，

边AO 在y 轴上，点1B ， 2B ， 3B ，…都在直线y x =上，则2017A 的坐标是（）

A. （2017，2017） ,2017)

C. (2017,2018) ,2019)

二、填空题

11．计算：tan45°﹣2cos60°=________．

12．在直角坐标系中，O 为原点，点A （a ，3）在第一象限，OA 与X 轴所夹的锐角为α，tanα=1.5，则b=_______.

13．在Rt △ABC 中，∠C ＝90°，且sin 30°＝12

，sin 45°sin 60°，cos 30°

，cos 45°，cos 60°＝12

；观察上述等式，当∠A 与∠B 互余时，请写出∠A 的正弦函数值与∠B 的余弦函数值之间的关系：______________．

14．若∠A 是锐角，且sinA 是方程2x 2－x ＝0的一个根，则sinA ＝________．

15．如图所示，BD⊥AC 于点D ， DE∥AB ， EF⊥AC 于点F ，若BD 平分∠ABC ，则与∠CEF 相等的角（不包括∠CEF）的个数是________.

三、解答题

16．计算：

(1) (2cos 45°－sin 60°)； (2)sin 60°·cos 60°－tan 30°·tan 60°＋sin 245°＋cos 245°.

17．如图，△ABC 中，∠ABC =60°，AB =2，BC =3，AD ⊥BC 垂足为D ．求AC 长．

18．如图所示，一测量员站在岸边的A 处，刚好正对河岸另一边B 处的一棵大树，这位测量员沿河岸向右走了50 m 到达C 处，在C 处测得∠ACB ＝38°，求河的宽度．(精确到0.01 m ，tan 38°≈0.7813)

19．在等腰直角三角形ABC 中， 90C ∠= ， 10AC =， D 是AC 上一点，若1tan 5

DBC ∠=，求AD 的长． 20．如图，矩形OABC 的两边在坐标轴上，点A 的坐标为（10，0），抛物线y=ax 2+bx+4

过点B ，C 两点，且与x 轴的一个交点为D （﹣2，0），点P 是线段CB 上的动点，设CP=t （0＜t ＜10）．

（1）请直接写出B 、C 两点的坐标及抛物线的解析式；

（2）过点P 作PE⊥BC，交抛物线于点E ，连接BE ，当t 为何值时，∠PBE 和Rt △OCD 中的一个角相等？

（3）点Q 是x 轴上的动点，过点P 作PM∥BQ，交CQ 于点M ，作PN∥CQ，交BQ 于点N ，当四边形PMQN 为正方形时，求t 的值．

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人教版九年级英语单元测试

人教版九年级英语单元测试 Company number【1089WT-1898YT-1W8CB-9UUT-92108】

九年级1-3单元测试一、单项选择(1.5*20=30) 1、Why not practice _________English in _________ English-speaking country? A. speaking, a B. speaking, an C. spoken, an D. speak, a 2、The more careful you are, ________mistakes you’ll make. A. fewer B. the fewer C. the less D. less 3. Good learners aren’t afraid _______mistakes. Instead, they learn ________mistakes. A. of making, in B. to make, from C. to make, in D. of make, from 4. For the first time, pay attention _________quickly to get the main ideas. A. to read B. reading C. to reading D. of reading 5.I discovered that listening to is the secret language learning. A. something interesting, to B. interesting something, to C. something interested, of D. interested something of 6. Why not ___ your teacher for help when you can’t finish _____ it by yourself? A. ask; write B. to ask; writing C. ask; writing D. asking; write 7. ___________exciting news! A. What B. What an C. How D. How an 8. Chang’e refused _________the magic medicine to Pang Meng. A. to give B. gave C. giving D. give 9. I’ve five pounds because I ate too much meat. A. put up B. put off C. put away D. put on 10. —Do you know if Jimmy to the party? —I am not sure. But if he , I will give him a big surprise. A. comes; will come B. will come; will come C. comes; comes D. will come; comes 11. Jenny keeps two pets. One is a dog, _________is a rabbit. A. another B. an other C. the other D. other 12. ---He dressed up ________a ghost last night. How scary! ---Take it easy! He just played a trick ________us. A. in, on B. in, in C. as, on D. as, in 13.— Can we visit Hong Kong this summer holiday? — I wonder it is the best time to go there. A. if B. when C. what D. how