### Introduction

We originally introduced trigonometry using right-angled triangles. However, the subject has applications in dealing with
**
any
**
triangles such as those that might arise in surveying, navigation or the study of mechanisms.

In this Section we show how, given certain information about a triangle, we can use appropriate rules, called the
**
Sine rule
**
and the
**
Cosine rule
**
, to fully ‘solve the triangle’ i.e. obtain the lengths of all the sides and the size of all the angles of that triangle.

#### Prerequisites

- have a knowledge of the basics of trigonometry
- be aware of the standard trigonometric identities

#### Learning Outcomes

- use trigonometry in everyday situations
- fully determine all the sides and angles and the area of any triangle from partial information

#### Contents

1 Applications of trigonometry to triangles1.1 Area of a triangle

1.2 The Sine rule

1.3 Use of the Sine rule

1.4 The ambiguous case

1.5 The Cosine rule