Download S3 Trigonometry

Maths Age 14-16
S3 Trigonometry
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Right-angled triangles
A right-angled triangle contains a right angle.
The longest side opposite
the right angle is called the
hypotenuse.
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The opposite and adjacent sides
The two shorter sides of a right-angled triangle are named
with respect to one of the acute angles.
The side opposite the
marked angle is called
the opposite side.
The side between the
marked angle and the
right angle is called
the adjacent side.
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x
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Similar right-angled triangles
If two right-angled triangles have an acute angle of the same
size they must be similar.
For example, two triangles with an acute angle of 37° are
similar.
5 cm
3 cm
6 cm
37°
10 cm
37°
4 cm
8 cm
The ratio of the side lengths in each triangle is the same.
opp
3
6
=
=
adj
4
8
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opp
3
6
=
=
hyp
5
10
adj
4
8
=
=
hyp
5
10
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Similar right-angled triangles
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Trigonometry
The word trigonometry comes from the Greek meaning
‘triangle measurement’.
Trigonometry uses the fact that the side lengths of similar
triangles are always in the same ratio to find unknown sides
and angles.
For example, when one of the angles in a right-angled triangle
is 30° the side opposite this angle is always half the length of
the hypotenuse.
12 cm
8 cm
6 cm
?
4 cm
30°
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?
30°
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The three trigonometric ratios
O
P
P
O
S
I
T
E
H
Y
P
O
T
E
N
U
S
E
θ
ADJACENT
Opposite
Sin θ =
Hypotenuse
SOH
Adjacent
Cos θ =
Hypotenuse
CAH
Opposite
Tan θ =
Adjacent
TOA
Remember: S O H C A H
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TOA
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Finding side lengths
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Finding angles
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