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


Sin θْ = opposite/hypotenuse

Cos θْ = adjacent/hypotenuse

Tan θْ = opposite/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


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


Trigonometry in Right-angled triangles – with diagrams