s2 CH 11 Introduction To Trigonometric Ratios Q
s2 CH 11 Introduction To Trigonometric Ratios Q
s2 CH 11 Introduction To Trigonometric Ratios Q
Opposite side Hypotenuse
C. D.
Hypotenuse Hypotenuse
Opposite side Adjacent side
Adjacent side Opposite side
c
a
b
a b a c
A. . B. . C. . D. .
b c c b
15
12
3 5 4 3
A. B. C. D.
5 4 5 4
9
x
35
1
5.If cos cos 72 cos 32 , find . (Correct your answer to 3 significant figures.)
4
A. 0.999 B. 1.00 C. 84.4 D. 84.434
8. In the figure, AXC is a straight line. Find AC. (Correct your answer to 3 significant figures.)
B
6 7
45 30
A C
X
9. In the figure, BCD is a straight line. Find AD. (Correct your answer to 1 decimal place.)
A
10
60
16 cm
20
B D
C
10. A pendulum swings back and forth as shown in the figure. Find . (Correct your answer to
3 significant figures.)
0.5 m
0.1 m
f
e
f g e e
A. . B. . C. . D. .
g f f g
39
15
36
12 5 5 12
A. B. C. D.
13 13 12 5
13. In the figure, ABC is a right-angled triangle where CAB 30 and BC 7. Find the length
of AC.
A
30
C B
7
3 14 1
A. B. C. D. 14
14 3 14
11
7
C
15. If 2sin sin 18 + sin 58, find . (Correct your answer to 3 significant figures.)
A. 35.3 B. 38.0 C. 42.6 D. 47.1
1
16. If sin( 40) , find .
2
A. 10 B. 30 C. 40 D. 70
18. In the figure, CDB is a straight line. Find . (Correct your answer to 3 significant figures.)
C
30
D
50
30
A B
A. 33.6 B. 34.8 C. 55.2 D. 56.4
19. In the figure, BCD is a straight line. Find x. (Correct your answer to 3 significant figures.)
A
x 11
37 85
B D
C
y
x
z
x z x z
A. . B. . C. . D. .
y x z y
36
4 3 3 4
A. B. C. D.
3 4 5 5
A C
7 3
23. If tan(3 + 15) tan 35tan 65, find . (Correct your answer to 1 decimal place.)
A. 13.8 B. 21.6 C. 56.3 D. 753.3
24. The following figure shows a right-angled triangle ABC where ABC 60, ABD 40.
Find AD. (Correct your answer to 1 decimal place.)
A
40 D
B 60 C
140 m
25. In the figure, BCD is a straight line. Find x. (Correct your answer to 1 decimal place.)
A
20
70 m
80 C
B D
x
8
C
8
A
9 D
27. In the figure, ABC and AED are straight lines. Find x. (Correct your answer to 3 significant
figures if necessary.)
D
x
15
30
A C
B 11
35 40
170 m
29. The figure shows a rectangle ABCD. Find . (Correct your answer to 3 significant figures.)
A B
8
10 14
D C
E 9
30. In the figure, ADBX is a rectangle. Find the distance between point D and the ground XC.
(Correct your answer to 3 significant figures.)
D
8m
B
A
2m 45
C
X
31. In the figure, a ladder leans against a vertical wall. When the foot of the ladder slides 5 cm
to the left, how far does the top of the ladder move vertically? (Correct your answer to
3 significant figures.)
40
60
5 cm
Level 1
1. Find the value of each of the following. (Correct your answer to 3 significant figures.)
(a) cos22 (b) sin35 (c) tan40
2. Find the value of each of the following. (Correct your answer to 3 significant figures.)
(a) sin43.6 (b) tan73.7 (c) cos88.8
3. Find the value of each of the following. (Correct your answer to 3 significant figures.)
(a) 2cos18 cos52 (b) 3sin42 5sin11 (c) 2tan10 3tan17
4. Find the value of each of the following. (Correct your answer to 3 significant figures.)
2 sin 15 cos 32 cos 58 3 tan 38
(a) sin 40 (b) (c)
sin 75 2 cos 70 tan 24 4 tan10
5. Find the value of each of the following. (Correct your answer to 3 significant figures.)
3 sin 12 cos18
(a) (b) (tan73 cos27)sin13 sin77cos13
5 tan 8
7. Find in each of the following. (Correct your answers to 1 decimal place if necessary.)
3 3 2
(a) tan (b) sin (c) cos
10 2 5
8. By considering the figure below, find the value of each of the following.
5
3
4
B
A 5 11
10
18
B
4
2 21
C C
A
A 13 C 12
13
8
105
B C
5 3
10
C 25 A
24 7
C B
12. By considering the figure below, find the value of each of the following.
9
40
41
7
3 10
B C B C
4 B 5 C 8
14. Find the value of in each of the following. (Correct your answers to 1 decimal place.)
(a) (b) (c)
A C
12 14 A
A
11
12 6
4
B B C C B
15. Find x in each of the following. (Correct your answers to 3 significant figures if necessary.)
(a) (b) (c)
A
A
A
12
10 x
x
16. Find x in each of the following. (Correct your answer to 3 significant figures.)
(a) (b) (c)
P
x 16
5 x
17. Find y in each of the following . (Correct your answer to 3 significant figures.)
(a) (b)
P
70 A
Q
13 20 21
y
y B
R C
Level 2
18. Find the value of each of the following. (Correct your answer to 3 significant figures.)
(4 sin 16 cos 70)(tan20 2 cos18)
(a) sin 90 cos 60
5 tan13 sin 19
(sin 30 cos 60 cos 45 tan 30) 2 (sin 45 cos 30) 2
(b)
(2 tan 60) 4
A
19. The figure shows ABC.
(i) cos .
(ii) sin
B 5 C
Q 7 R
5
3
B C
3
5
(a) Find the length of AC.
(b) Find the values of sin and cos . A
(Express your answers in surd form.)
C
P
23. The figure shows PQR.
x
(a) Find the length of PQ. (Express your answer in surd form.) Q
(b) Find the value of tan x. (Express your answer in surd form.)
6
(c) Find x and y. (Correct your answer to 3 significant figures.)
5
24. The figure shows ABC where AD CB, CAD = 40, ABD = 30, AB = 5. Find the length
of AC. (Correct your answer to 3 significant figures.)
A
40 5
30
C D B
B
(a) Find x.
(b) Find the length of BC.
(c) Find the length of CD.
(Correct your answers to 3 significant figures if necessary.)
26. In the figure, PSR is a straight line, PQ PR, PQS 50, PRQ 30, PQ 5.
P
5
S
50
R 30 Q
27. In the figure, the slope makes an angle of 20 with the horizontal ground. Eason walks 300 m
up the slope from O to H. Find his vertical distance from the ground ( HG). (Correct your
answer to 3 significant figures.)
H
300 m
20
G O
28. Students A, B and C try to measure the width of a river by using a measuring tape of 10 m
long and a protractor. Student A stands at point P, student B stands at point Q, and student C
uncoils the measuring tape and reaches point R so that PR = 10 m and QPR = 90. If
PRQ i s measur ed t o be 61.7 , f i nd t he wi dt h of t he r i ver. ( Cor r ect your answer t o
3 significant figures.)
61.7
10 m
Q
P
29. Kelly and Anita try to measure the height of Yee Woo Building by using a measuring tape and
a bamboo pole. Kelly lies on the floor at point E which is 30 m from the building. She looks at
the top T of the building. Anita moves the bamboo pole from point E towards the building
until the tip of the bamboo pole Q, points E and T form a straight line. If EP = 1.7 m and the
length of the bamboo pole is 1 m, find the height of Yee Woo Building. (Correct your answer
to 3 significant figures.)
T
Level 3
30. The figure shows PQR where PQ a, QR = b, PR c, PQ QR, PRQ , RPQ .
P
c
a
R b Q