# Introduction

This book is a *tour de force* of right-angled triangles,
efficiently teaching all that a General Certificate of Secondary Education
(GCSE) student needs to know about this subject.

The emphasis is on teaching the subject rather than teaching the exam, and introducing the student to the idea of proof and formal presentation (with judicious diagrams). It should be accessible, and at the same time moderately challenging, to any student of mathematics at this level.

It is particularly suited for students wishing to consolidate their understanding of trigonometry and geometry of right-angled triangles, and for teachers looking for alternative approaches to presenting the subject matter.

# Contents

The book comprises of

- 22 pages (plus front-matter, preface, contents, and index)
- 13 chapters (plus answers to exercises)
- 32 figures
- 23 exercises.

The subjects covered include:

- Full explanation of the
*cosine*function - Definition of the
*sine*and*tangent*functions in terms of cosine - Use of a calculator (especially of the
*polish*variety) to obtain approximate values for trigonometric functions - Definition of area of plain figures
- Derivation of the area of a right-angled triangle
- Proof of the constancy of the sum of internal angles
- Similar triangles explained through progressive examples
- Elementary algebra of squares and of square roots
- Pythagoras' Theorem is described, its application illuminated by example
- Standard triangles (extra information for GCSE students):
- 3-4-5 triangle
- 60° triangle
- 45° triangle

# Availability

The book is only available on-line as an e-book. It may be obtained:

** The book was re-published in July 2012 with some small corrections
and very minor clarifications.*