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© Boardworks Ltd 20151 of 9
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© Boardworks Ltd 20152 of 9
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.
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.
The ratio of the side lengths in each triangle is the same.
34
=68
oppadj
=45
=810
adjhyp
=35
=610
opphyp
=
3 cm
4 cm
5 cm
37°
8 cm
6 cm10 cm
37°
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Similar right-angled triangles
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The sine ratio
The ratio of the length of the opposite sidethe length of the hypotenuse
is the sine ratio.
The value of the sine ratio depends on the size of the angles in the triangle.
θ
OPPOSITE
HY
PO
TE
NU
SE
sin θ =opposite
hypotenuse
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The cosine ratio
The ratio of the length of the adjacent sidethe length of the hypotenuse
is the cosine ratio.
The value of the cosine ratio depends on the size of the angles in the triangle.
θ
cos θ =adjacent
hypotenuse
A D J A C E N T
HY
PO
TE
NU
SE
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The tangent ratio
The ratio of the length of the opposite sidethe length of the adjacent side
is the tangent ratio.
The value of the tangent ratio depends on the size of the angles in the triangle.
θ
OPPOSITE
tan θ =oppositeadjacent
A D J A C E N T
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