Download Boardworks Maths Trigonometry W8

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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°
4 cm
10 cm
37°
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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The sine ratio
the length of the opposite side
is the sine ratio.
the length of the hypotenuse
The ratio of
The value of the sine ratio depends on the size of the angles
in the triangle.
O
P
P
O
S
I
T
E
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H
Y
P
O
T
E
N
U
S
E
opposite
sin θ =
hypotenuse
θ
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The cosine ratio
the length of the adjacent side
The ratio of
is the cosine ratio.
the length of the hypotenuse
The value of the cosine ratio depends on the size of the
angles in the triangle.
H
Y
P
O
T
E
N
U
S
E
adjacent
cos θ =
hypotenuse
θ
ADJACENT
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The tangent ratio
the length of the opposite side
The ratio of
is the tangent ratio.
the length of the adjacent side
The value of the tangent ratio depends on the size of the
angles in the triangle.
O
P
P
O
S
I
T
E
tan θ =
opposite
adjacent
θ
ADJACENT
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