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第一章 直角三角形的边角关系(A 卷·提升卷)
班级___________ 姓名___________ 学号____________ 分数____________
考试范围:全章的内容; 考试时间:120 分钟; 总分:150 分
一、选择题(本大题共12 小题,每小题3 分,共36 分)
1ABC AB
sinA
cosB
ABC
A
B
C
D
!"cosB
#B30°
"sinA
#A30°
"A+B+C180°
#C180$%30$%30$120°
#ABC
&'!B
2 RtACB C90°AB8
AC ()
A6
B7.5
C8
D12.5
! RtACB
"cosA
#AC6
&'!A
3*+,-ABC ./
01233/ sinA 4)
A
B
C
D
!56 DC
72389!CD:AB
DC
AC
& sinA
&'!D
4*+;<=>?@ 20°;<A;<A AC () 200 B;<A@.C@DEFG AB
()B
A
B
C200cos20°
D200sin20°
!"
#ABAC•sinC200sin20°
&'!D
5*+?IJKL0M1NO/ A PQ9RS M MTU 40$1LJKVWXY 20 Z[\GN
O 48 ]^_0`CaRS M 0b1L B PcdYJKFRS M efZ[
A960tan40°
B960cot40°
C16tan40°
D16cot40°
!ghij9ABM90°A40°AB20×
16Z[
#BMAB•tan40$16tan40°Z[
!dYJKFRS M ef
16tan40$Z[
&'!C
6lmnop“rs&[”ursXvrswxyz=/ P P{| 400 BAw\u*+,-
uA AB )bU1LuA}/ A ~/ P MTU 30°1L/ B ~/ P MTb 60°1L
AB400 B/ P CuA AB ef
h!
A
B
C87
D173
!/ P PC:AB) C
PCx B
RtAPC APC30°
#
B
RtCBP CPB60°
#
B
"AB400 B
#AC+BC400
#
#
#PC173 B
#/ P CuA AB ef) 173 B
&'!D
7*+ RtABC BAC90° AB6AC8/ D
AC ?/
sinDBC
4)
A
B
C
D
!*+! D DE:BC) E
"
#AD3CD
"ACAD+CD
#83CD+CD CD2
#AD6
"AB6BAC90°
#
" RtABC BAC90°AB6AC8
#
"
#
#
&'!B
8*+ABC C90°V/ B )yBC () AB / D]V/ CD )
yBC ()/ E BC5
CF ()
A
B3
C
D
!7i
BF ]ABC
/ F AB ) M
RtABC
cosA
AC12xAB13x
12x2+5213x2
9 x1
,V AC12BC13
¡) BF ]ABCC90°FM:AB
,V CFMF
SABCSABF+SBCF
,V CF
&'!A
9*+¢ AB 1L£¤ BDV¤¥¦ BD §¨©ª« BC ¬ DCQ9/ C / B Tb 60$1
L/ D U1LBC1800mª« DC ()
A900m
B
C
D1800m
!*+/ C CE:BD) E
7ij9!EBF90°CDE45°CBF60°
#CBEEBF%CBF30°
RtBCE BC1800m
#CE
BC900m
RtCDE DCE45°
#CD
900
m
#ª« DC () 900
m
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Bxx%10cos50°
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Dxx+10sin 50°
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Ê
#HECD10CEDH
#FHx%10
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#DHFHx%10
#CEx%10
"tanβtan50$
#xx%10tan 50°
&'!A
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A
B
C
D
!*+ OH:AB H
7ij!AB8OA%OH3
"OH:AB
#AHBH4
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#42OA+OHOA%OH
#OA+OH
#OA
OH
#cosOAB
&'!B
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v*+,-“ôõà+”56 EGDG01 ABCD æ EFGH É(çČ)
!1 sin
DGE å
A
B
C
D
!/ D ND:GE GE č(/ N
7ij¥ÿ01çĎ
4 ÿÂå
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xX01É() x
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b
7ij9!
9!
GDE EG
GH
b NEND
ED
b
xEG
GH
a%b
x
tanDGE
sinDGE
&'!A
二、填空题(本大题共4 小题,每小题4 分,共16 分)
13ABC þB55°C95°ĐđA 0à4å
!"B55°C95°
#A180$%55$%95$30°
#sinAsin30$
&Ē)!
14*+ÀēÁĔ/ Pm8ĕnĖėº OP æ x Ę Ęę α 0Ě4)
m 4)%6
!/ P PA:x x Ę/ A
7ij89!PA8OA|m|%m
"α 0Ě4)
#tana
#m%6
&Ē)!%6
15*+“ě”ABCD
BC16ABC30°/ D C AB ef)
2
!č( CD AB / E/ E EG:BC / G/ D DF:BA / F*+
"BC30°
#CEAB+C60°BECE
Ĝ EG:BC
#BGCG8
#BE
#AEAB%BE8
ĜEDA90°A30°
#ADcos30°×AE
×
4
#DF
AD
2
D C AB ef) 2
&Ē)!2
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ĵjABC º?/ D Ķ123/ D ķĸABC ĝĞğ/*+ 2åĹABC
ABAC/ D )ABC ĝĞğ/AD9
DB+DC 4) 10
!/ A AE:BC*+,-!
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#
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#
# BEm
BC2m
#ghéêë9!
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ABC ĝĞğ/
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#ABCACB
#2+ABD3+BCD
#ABDBCD
#ABDĺBCD
#
#
9!BD6CD4
#BD+CD6+410
&Ē)!10
三、解答题(本大题共9 小题,共98 分)
17ÜÎ!
!|2%
|+2%2%
0+tan60°
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É BC sinDAB
BD3
!
1AB (Ļ
2CAB ļĚ4
!1/ D DE:AB / E
RtBDE DE:AB
B45°
#
RtADE
DE3
#
AD5
#
#ABAE+BE4+37
2 CH:AB) H
#BC2BD6
"ABC45°
#
#AH7%61
RtCHA
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íŃŀg¹/ A ¢ĽŁLńł 10m Ca/ C PQ9pŀ.¦ B Ņ) 45°ņŇLńł 20m
Ca/ D PdY/ D ¬pŀ.¦ B ?Äňʼnpŀ AB FG¬ĽŁ@Č
gŊ
!*+56 BD/ C CE:AB / ECF:AF / F CFAEAFCE
ghij9!CEŋBDAC10mCD20mBCE45°
#
BE2AE
RtBCE BCE45°
#BCE
åĹ
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#
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Ļ
AEx m CE2AE2x m
RtACE AC2AE2+CE2
#102x2+2x2
9!x2
AE2
#ABAE+CE6
20Ō!ABC ÑĊōA âÉæC âÉČķĸA Ŏàŏ thiA thiA
Ő®Æci!
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2 thiA
A60 ő 120°Ļ
3A
Œœ thiA æ sinA ½ÃĔ
!*+ BH:AC) H
1 RtBHC sinC
BC2BH
RtBHA sinA
AB
BH
#thiA
Ļ
2"thi A
#
"C30°
#tan30$
#ABC90°
#A60°
*+ghâŔŕAŖBC
YBŖAC120°
&Ē)!60 ő 120Ļ
3ABC thiA
RtBHA sinA
RtBHC sinC
BC2BH
#thiA2sinA
21ŗXŘřŚśŜłŝާşAŠAŠÃšY*+ 1ÈÉ ABCD )ÊAB ( 3 BAD ( 1 B
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ŮůşXŘŰŐűíë7h!sin36$Ų0.59cos36$Ų0.81tan36$Ų0.73
!7ij9!AD:DEPE:DE
#ADŋPEPED90°
"ADC36°
#DPE36°
"PE1.6 B
#DEPE•tanDPEŲ1.6×0.731.168B
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#CD3B
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