Application of Sine Rule, Cosine Rule and Area of a Triangle

Sine rule

a/sin A = b/sin B = c/sin C or sin A/ a = sin B/ b = sin C/ c

Conditions that allow the sine rule to be used

-two angles and one side are known -two sides and one non-included angle are known

Example of included angle

Angles contained by two sides (both sides are known for their value)

Example of non-included angle

An angle of which only one side is known for its value

Cosine rule

Conditions that allow the cosine rule to be used

-two sides and an included angle are known -three sides are known

Area = 1/2× base × height

Area = 1/2ab sin C = 1/2ac sin B = 1/2bc sin A

Area of a triangle using Heron’s formula

where a, b and c are the sides of the triangle and s = (a + b + c)/2

Ambiguous case

Two triangles can be constructed by using the same set of information given