Download S.2 Mathematics Chapter 11 Trigonometric Ratio Worksheet for

S.2 Mathematics
Chapter 11 Trigonometric Ratio
Worksheet for Section 11.1 Sine Ratio
Worksheet 1: Right-angled triangle with a given acute angle 30o
The figure below shows a right-angled triangle ABC, where B =  and C = 90.
Part 1
Measure the length of the opposite sides and the hypotenuses by a ruler for the following right-angled triangles
with a given acute angle 30o of different size. Calculate their ratio and complete the following table.
Example
1.
2.
N
E
B
A
C
3.
F
D
4.
Q
O
M
5.
S
T
P
Y
X
Z
R
U
Example
opposite side
（cm）
hypotenuse
（cm）
1
2
Ratio of opposite side to
hypotenuse (Answer in decimal number)
1
 0.5
2
1.
2.
3.
4.
5.
S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet
Page 1
Part 2
From the data obtained from the table above, we have:
For all right-angled triangles having the same acute angle 30o, their ratios of the opposite
side to the hypotenuse are equal to __________, regardless of the sizes of the triangle.
i.e.
opposite side
for 30o  ______
hypotenuse
Part 3
Let’s Think
1.
For a right-angled triangle with a given acute angle 30o, Can you find the following values without
measurement by ruler?
(a) Length of the
opposite side
□ Yes, Answer = __________
□ No
(b) Length of the
hypotenuse
□ Yes, Answer = __________
□ No
(c) Ratio of the opposite
side to the hypotenuse
□ Yes, Answer = __________
□ No
2.
From the result obtained from Part 2, is it true for all right-angled triangles with different acute
angles?
□ Yes
or
□ No
Worksheet 2: The Ratio of the opposite side to the hypotenuse for different acute angles (Sine Ratio)
Part 1
A right-angled triangle will be shown on the screen. We drag the red point on the right hand side to change the
size of the right-angled triangle. And then we drag the green point on the left hand side to change the angles of
the right-angled triangle.
Drag the red point to change the size of the right-angled triangle.
Drag the green point to change the angles of the right-angled triangle.
opposite side = 0.5
hypotenuse = 1
the ratio = 0.5
Part 2
The ratio of the opposite side to the hypotenuse for different angles will be shown on the screen. Complete the
following table.

opposite side
hypotenuse
5o
10o
15o
20o
25 o
30 o
35 o
40 o

opposite side
hypotenuse
45o
50o
55o
60o
65 o
70 o
75 o
80 o
S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet
Page 2
Part 3
From the data obtained from the table in Part 2, we have the following observation.
1.
2.
opposite side
will
hypotenuse
opposite side
When 0o <  < 90o, the ratio of
lies between
hypotenuse
When  increases, the ratio of
.
and
.
Part 4
By using the table in Part 2, find the unknown in each of the following right-angled triangles.
(Give the answer correct to 1 decimal place.)
Example:
Solution:
x
 0.5
4
x = 0.54 = 2
4.
1.
5.
2.
6.
12.7

12.5
3.
Let us think:
1.
2.
S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet
Page 3
Worksheet 3: Calculator and the Sine Ratio
For any right-angled triangle,
Part 3
Use a calculator to find the unknown in each of the
following right-angled triangles.
(Give the answer correct to 3 significant figures.)
Example:
The ratio of the opposite side to the hypotenuse for a
given acute angle  is called the sine ratio of . It is
denoted by sin  and
opposite side
sin 
hypotenuse
Part 1
By using a calculator, find the following value.
angle 
(2 d.p.)
5°
15
0.2
x
43o
1.
x = 15sin43o
x = 10.2
10.5
78o
sin  (i.e. sine ratio)
(4 d.p.)
20°
23°
Solution:
x
 sin 43o
15
y
2.
0.6
0.8
61°
0.9
0.95
82°
2
If the value of sin  is given, we
can find out the acute angle  by a
calculator.
1. Set the calculator to degree
mode first.
2. Press the SHIFT and sin
keys, then enter the sine ratio.
3. Press the EXE key.
1
If the value of angle  is given,
we can find out the sine ratio
of a given angle  (i.e. sin ).
1. Set the calculator to
degree mode first.
2. Press the sin key and
enter the angle.
3. Press the EXE key.
3.
Part 2
Do the following questions on your C.W. book.
1.
2.
3.
4.
5.
By using a calculator, find the values of the following
expressions correct to 4 significant figures.
(a) sin 43 – sin 28 (b) 2 sin 11
By using a calculator, find the values of the following
expressions correct to 4 decimal places.
(a) sin 66
(b) sin 32.48
(a) By using a calculator, find the value of
sin 34 + sin 26  sin 60 correct to 3 significant
figures.
(b) From the result obtained in (a), is sin 34 + sin
26 equal to sin (34 + 26)?
Find the acute angle  in each of the following using a
calculator. (Give your answers correct to 3 significant
figures.)
(a) sin  = 0.22
(b) sin  = sin 68 – sin 40
Find the acute angles  in the following using a
calculator.
(a) sin  0.62, correct to the nearest degree.
(b) sin =(1/5) sin 35, corr. to the nearest 0.1.
(c) 7 sin = 3, corr. to 3 significant figures.
4.
5.
Part 4
Do Ex.11A Q.13-18 (P.180) on your C.W. book.
S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet
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