### Introduction

Right-angled triangles (that is triangles where one of the angles is $9{0}^{\∘}$ ) are the easiest topic for introducing trigonometry. Since the sum of the three angles in a triangle is $18{0}^{\∘}$ it follows that in a right-angled triangle there are no obtuse angles (i.e. angles greater than $9{0}^{\∘}$ ). In this Section we study many of the properties associated with right-angled triangles.

#### Prerequisites

- have a basic knowledge of the geometry of triangles

#### Learning Outcomes

- define trigonometric functions both in right-angled triangles and more generally
- express angles in degrees
- calculate all the angles and sides in any right-angled triangle given certain information

#### Contents

1 Right-angled triangles2 Engineering Example 1

2.1 Noise reduction by sound barriers

3 Engineering Example 2

3.1 Horizon distance

3.2 Inverse trigonometric functions (a first look)

4 Solving right-angled triangles

5 Engineering Example 3

5.1 Vintage car brake pedal mechanism