Trigonometry: sine (including exact values) 1
F/H
*
1
Here are some similar triangles.
2cm
30º
1a
1cm
30º
30º
Use the triangles to complete this table.
Angle
Opposite (cm)
Hypotenuse (cm)
Opposite ÷
Hypotenuse
30º
1
2
1 ÷ 2 = 0.5
30º
2
30º
1b
6
Complete this table.
Angle
Opposite (cm)
30º
4
30º
5
30º
1c
Opposite ÷
Hypotenuse
Hypotenuse (cm)
12
Here is a right-angled triangle.
y
7cm
1d
Here is a right-angled triangle.
16cm
Not drawn
accurately
30º
Work out the value of y.
Answer
Mind The Gap Toolbox
w
Not drawn
accurately
30º
Work out the value of w.
Answer
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1
Trigonometry: sine (including exact values) 2
F/H
*
1
Here are some similar triangles.
2 cm
1 cm
45º
1a
45º
45º
Use the triangles to complete this table.
Angle
Opposite (cm)
Hypotenuse (cm)
Opposite ÷
Hypotenuse
45º
1
2
1
2
45º
2
3 2
45º
1b
Complete this table.
Angle
Opposite (cm)
30º
4
30º
5
6 2
30º
1c
Opposite ÷
Hypotenuse
Hypotenuse (cm)
Here is a right-angled triangle.
y
7 cm
1d
Not drawn
accurately
Here is a right-angled triangle.
8 2 cm
45º
Work out the value of y.
Answer
Mind The Gap Toolbox
w
Not drawn
accurately
45º
Work out the value of w.
Answer
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2
Trigonometry: sine (including exact values) 3
F/H
*
1
Here are some similar triangles.
2 cm
3 cm
60º
1a
60º
60º
Use the triangles to complete this table. Give your answers to 3 decimal places.
Angle
Opposite (cm)
Hypotenuse (cm)
3
60º
4
3 3
60º
1b
3
2
2
60º
Opposite ÷
Hypotenuse
1c
Here is a right-angled triangle.
8 cm
y
60º
Work out the value of y.
Answer
Mind The Gap Toolbox
Not drawn
accurately
Here is a right-angled triangle.
w
5 3 cm
Not drawn
accurately
60º
Work out the value of w.
Answer
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3
Trigonometry: sine (including exact values) 4
F/H
*
Give your answers to one decimal place. Diagrams not drawn accurately.
1
Here is a right-angled triangle.
5 cm
4 Here is a right-angled triangle.
w
y
1.3 cm
15º
40º
Work out the value of w.
Work out the value of y.
Hypotenuse
Sin θº
× sin 40º =
2
Opposite
Opposite
÷
cm
3
1.7 cm
Work out the value of angle z.
Sin θº
Opposite
=
Opposite Hypotenuse
cm
÷
sin -1
Angle
º
=
6 Here is a right-angled triangle.
Here is a right-angled triangle.
w
4.4 cm
1.8 cm
1.9 cm
z
25º
Work out the value of w.
Opposite
cm
z
Work out the value of y.
×
=
5 cm
y
20º
Hypotenuse
Hypotenuse
5 Here is a right-angled triangle.
Here is a right-angled triangle.
5 cm
Sin θº
Sin θº
÷
Mind The Gap Toolbox
Work out the value of angle z.
Opposite Hypotenuse
Hypotenuse
=
cm
sin -1
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÷
=
Angle
º
4
Trigonometry: sine (including exact values): Test
F/H
*
1
Here is a right-angled triangle.
4 cm
Not drawn
2 cm accurately
z
Work out the value of angle z.
Answer
2
º
Here is a right-angled triangle.
10 cm
y
Not drawn
accurately
20º
Work out the value of y.
Give your answer to one place of decimals.
Answer
3
cm
Here is a right-angled triangle.
w
9 cm
Not drawn
accurately
25º
Work out the value of w.
Give your answer to one place of decimals.
Answer
Mind The Gap Toolbox
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cm
5
Trigonometry: sine (including exact values): Answers
F/H
*
Trigonometry sine 1
1a
Angle
Opposite (cm)
Hypotenuse (cm)
Opposite ÷
Hypotenuse
30º
1
2
1 ÷ 2 = 0.5
30º
2
4
2 ÷ 4 = 0.5
30º
3
6
3 ÷ 6 = 0.5
Angle
Opposite (cm)
Hypotenuse (cm)
Opposite ÷
Hypotenuse
30º
4
8
4 ÷ 8 = 0.5
30º
5
10
5 ÷ 10 = 0.5
30º
6
12
6 ÷ 12 = 0.5
Hypotenuse (cm)
Opposite ÷
Hypotenuse
1b
1c y = 14 cm!
1d w = 8 cm
Trigonometry sine 2 Answers
1a
Angle
Opposite (cm)
45º
1
2
1
2
45º
2
2 2
1
2
45º
3
3 2
1
2
Angle
Opposite (cm)
30º
4
4 2
1
2
30º
5
5 2
1
2
30º
6
6 2
1
2
1b
1c y =
Hypotenuse (cm)
Opposite ÷
Hypotenuse
7 2 cm! 1d w = 8 cm
Mind The Gap Toolbox
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6
Trigonometry: sine (including exact values): Answers
F/H
*
Trigonometry sine 3
1a
Angle
Opposite (cm)
3
60º
1b y =
Hypotenuse (cm)
2
60º
2 3
4
60º
3 3
6
Opposite ÷
Hypotenuse
3
2
3
2
3
2
4 3 cm! 1c w = 10 cm
Trigonometry sine 4
1
2
3
4
5
6
5 × sin 40 = 3.2 cm
5 × sin 20 = 1.7 cm
1.8 ÷ sin 25 = 4.3 cm
1.3 ÷ sin 15 = 5 cm
sin−1(1.7 ÷ 5) = 19.9º
sin−1(1.9 ÷ 4.4) = 25.6º
Trigonometry sine Test
1
2
3
30º
10 ÷ sin 20 = 29.2 cm
9 ÷ sin 25 = 21.3 cm
Mind The Gap Toolbox
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7