Download UNIT 15 Trigonometry Extra Exercises 15.1

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UNIT 15 Trigonometry
Extra Exercises 15.1
Give all answers to 3 significant figures, unless otherwise stated.
1.
Calculate the length of the unknown side in each of the following triangles:
(a)
(b)
8 cm
17 cm
11 cm
14 cm
(c)
(d)
9 cm
16 cm
20 m
5m
2.
A rectangle has sides of length 14 cm and 7 cm.
Calculate the length of a diagonal of the rectangle.
3.
A ship sails 100 km north and then 200 km east.
How far is the ship from its starting point?
4.
Calculate the area and perimeter of this trapezium:
8 cm
6 cm
4 cm
5.
A square has a diagonal of length 40 cm.
Determine the length of the sides of the square.
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5 cm
MEP: Demonstration Project
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UNIT 15 Trigonometry
1.
Extra Exercises 15.2
Calculate sin θ for each of the following triangles. Comment on the values you obtain.
(a)
(b)
2 cm
14 cm
1 cm
3.
142 cm
7 cm
71 cm
θ
θ
2.
(c)
θ
Use your calculator to determine the following, correct to 4 decimal places:
(a)
sin 72 °
(b)
tan 33 °
(c)
cos 3.6 °
(d)
sin 13.9 °
(e)
tan 24.7 °
(f)
cos 45 °
Use your calculator to determine θ , correct to 1 decimal place, if:
(a)
sin θ = 0.7
(b)
cosθ = 0.4
(c)
tan θ = 14
(d)
cosθ = 0.6
(e)
sin θ = 0.9
(f)
tan θ = 0.1
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MEP: Demonstration Project
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UNIT 15 Trigonometry
Extra Exercises 15.3
Give all answers to 3 significant figures, unless otherwise stated.
1.
Calculate the lengths of the sides marked with letters in each of the following diagrams:
b
(a)
(b)
44 cm
y
a
14 cm
28˚
x
62˚
8 cm
(c)
(d)
52˚
25˚
15 m
h
a
2.
A rectangle has sides of length 18 cm and x cm . The acute angle between the diagonals
of the rectangle is 40 ° . Determine x .
3.
A pole of length 6 m leans against a vertical wall.
The angle between the pole and the horizontal is 70 ° .
Calculate the height of the top of the pole.
4.
Determine the length of the base of the triangle shown.
50˚
8 cm
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8 cm
MEP: Demonstration Project
Teacher Support Y9B
UNIT 15 Trigonometry
1.
Extra Exercises 15.4
Calculate the size of the angle θ , marked in each triangle. Also calculate the length of
the unknown side of each triangle. Give your answers to 3 significant figures.
(a)
(b)
12 cm
15 cm
θ
40 cm
θ
8 cm
(c)
15 cm
(d)
8m
12 cm
θ
θ
20 m
A
2.
In the diagram shown, calculate the
angles α and β if the diagonal BD
has length 10 cm. Give your
answers to 1 decimal place.
8 cm
8 cm
D α
B
12 cm
12 cm
β
3.
A right angled triangle has sides of length 5 m, 12 m and 13 m.
C
Calculate, to 1 decimal place, the sizes of the angles of this triangle.
4.
An isosceles triangle has sides of length 8 cm, 8 cm and 6 cm.
Determine the sizes of the angles in this triangle, to 2 significant figures.
5.
Calculate the size of the acute angle between the two diagonals of a rectangle which has
sides of length 8 cm and 12 cm. Give your answer to 3 significant figures.
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Extra Exercises 15.1 Answers
1.
(a)
16.1 cm
2.
15.7 cm
3.
224 km
4.
46.9 cm 2 ,
5.
28.3 cm
(b)
20.2 cm
(c)
19.4 cm
(d)
13.2 cm
34.5 cm
Extra Exercises 15.2 Answers
1.
(a) 0.5
(b) 0.5
(c) 0.5
Always the same because θ is the same angle.
2.
(a)
(d)
0.9511
0.2402
(b)
(e)
0.6494
0.4599
(c)
(f)
0.9980
0.7071
3.
(a)
44.4 °
(b)
66.4 °
(c)
85.9 °
(d)
53.1 °
(e)
64.2 °
(f)
5.7 °
(b)
a = 6.6 cm,
Extra Exercises 15.3 Answers
1.
(a)
x = 38.8 cm,
(c)
h = 13.0 cm
2.
6.55 cm
3.
5.64 m
4.
6.76 cm
y = 20.7 cm
(d)
b = 12.4 cm
a = 35.5 cm
Extra Exercises 15.4 Answers
Angle θ :
(a)
57.8 °
(b)
16.7 °
(c)
51.3 °
(d)
23.6 °
Side length:
(a)
12.7 cm
(b)
41.8 cm
(c)
19.2 cm
(d)
18.3 cm
2.
α = 116.7 ° ,
β = 49.2 °
3.
67.4 °,
4.
44 °,
5.
67.4 °
1.
22.6 °,
68 °,
90 °
68 °
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