Introducing the Sine and Cosine Rule Solving Rightangled

Introducing the Sine and Cosine Rule

Solving Right-angled Triangles When we are given some information about a right-angled triangle, we can determine the missing sides or angles using one of the following mathematical techniques. • Pythagoras Theorem to work out the length of one of the sides given the length of the other two sides. • Trigonometric ratios (sine, cosine and tangent) to work out • the angle given two of the sides • a side given one side and one angle

The Sine and Cosine Rules If a triangle is not right-angled, we can use one of two rules. • The Sine rule, which is used to work out • the length of a side given two angles and a side • the length of a side given two sides and an angle which is not between them • The Cosine rule, which is used to work out • the length of the third side of a triangle given the length of two sides and the angle between them • the size of an angle given the length of the three sides

Anatomy of a triangle The basic anatomy of a triangle is shown here. The lower case letters represent the lengths of the line segments that form the sides of the triangle; upper case letters are the angles. We say that side a is opposite angle A, side b is opposite angle B and side c is opposite angle C. Each point is called a vertex.