An introduction to Trigonometry

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An introduction to Trigonometry
A
2
An introduction to Trigonometry
Opposite
A
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An introduction to Trigonometry
Hypotenuse
Opposite
A
4
An introduction to Trigonometry
Hypotenuse
Opposite
A
Adjacent
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Example Label each of the following
triangles (i) (ii) (iii)
g
d
f
b
a
i
h
e
c
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• Example
• For the triangle below
• Write down the lengths of the opposite and
  hypotenuse sides
• Work out the ratio

Opposite 8cm Hypotenuse 12cm
12cm
8cm
41.8
c) Now work out the sin of 42 using the
calculator
Sin 41.80.6665
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Right-angled Trigonometry
Opp
Hyp
A
Adj
8
Example Work out the lettered length in the
triangle given below, giving your answer to 1
decimal place.
8 cm
a
25
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Example Work out the lettered length in the
triangle given below, giving your answer to 1
decimal place.
15 m
48
b
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Example Work out the lettered length in the
triangle given below, giving your answer to 2
decimal place.
15
37 cm
b
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Example Work out the length of AB in the
triangle given below, giving your answer to 2
decimal place.
A
56
C
B
7 m
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• Example
• For the triangle below
• Write down the lengths of the Adjacent and
  hypotenuse sides
• Work out the ratio

12cm
Adjacent 7cm Hypotenuse 12cm
54.3
7cm
c) Now work out the cos of 54.3 using the
calculator
cos 54.30.5835
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Right-angled Trigonometry
Opp
Hyp
A
Adj
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Example Work out the lettered length in the
triangle given below, giving your answer to 1
decimal place.
10 cm
31
a
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Example Calculate the length of PQ in the
triangle PQR
P
R
52 cm
32?
Q
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• Example
• Calculate the length XY in the triangle XYZ

X
Y
59?
4.6 cm
Z
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Right-angled Trigonometry
Opp
Hyp
A
Adj
18
Example Work out the lettered length in the
triangle given below, giving your answer to 1
decimal place.
4 cm
27
a
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• Example
• Calculate the length YZ in the triangle XYZ,
  giving your answer correct to 3 significant
  figures.

Y
Z
38?
4.6 cm
X
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Example Work out the length of AC in the
triangle given below, giving your answer to 2
decimal place.
A
56
C
B
7 m