Trigonometry and Right-angled Triangles
You should know how to use the trigonometric ratios (sine, cosine
and tangent) in order to solve problems with right-angled triangles.
Hypotenuse – the longest side of a right-angled triangle, it is
always the side opposite the right-angle
Opposite – the side opposite the known angle or the angle you
are looking for
Adjacent – the side forming the known angle or angle you are
looking for with the hypotenuse
65ْ
Hypotenuse
Adjacent
Opposite
Sin θْ = opposite/hypotenuse
Cos θْ = adjacent/hypotenuse
Tan θْ = opposite/adjacent
Hypotenuse
Opposite
θْ
Adjacent
These can easily be rearranged if you want to find the length of
one of the sides:
opposite = hypotenuse x Sin θْ
hypotenuse = opposite/ Sin θْ
adjacent = hypotenuse x Cos θْ
hypotenuse = adjacent/ Cos θْ
opposite = adjacent x Tan θْ
adjacent = opposite/ Tan θْ
b
b = 4/cos 37ْ
a
a = 4 x tan 37ْ
37ْ
4
6
βْ
sin αْ = 6/7
α = sin-1 (6/7)
α = 59ْ
3.6
7
αْ
cos βْ = 6/7
β = cos-1 (6/7)
β = 31ْ
Given a right angled triangle and two additional pieces of
information about the triangle (ie one side length and one of the
other angles, or two side lengths) you should be able to find the
size of all the angles and the lengths of all the sides
If you know the size of all 3 angles of a triangle, but none of the
lengths, then you cannot calculate the lengths. If you consider
similar triangles, you will realise why the lengths cannot be
calculated.