Trigonometry in all triangles

The sine rule and cosine rule can be used with any triangle, including right-angled triangles.

You should know how to use the sine rule and the cosine rule.

You should know when to apply the sine rule and when to apply the cosine rule.

 Sine rule

a/sinA = b/sinB = c/sinC


sinA/a = sinB/b = sinC/c

 Cosine rule

a2 = b2 + c2 – 2bc cosA


cosA = (b2 + c2 – a2)/2bc

The Formulae Booklet in the exams will only give the cosine rule in the first form (for finding a side length), so you need to be able to rearrange it into the second form (for finding an angle).

 Area of a triangle

Area = ½ base x height

This formula is most useful where the triangle is right-angled or you know the perpendicular height of the triangle.


Area = ½ ab sinC

This formula for the area of a triangle can be used if you know the lengths of two sides and the size of the angle between them.


Trigonometry in all triangles – with diagrams