ESM Chapter 3 - Pythagoras' theorem and trigonometry · 134 Chapter 3 PythagorasÕ theorem and...

Chapter 3 Pythagoras’ theorem and trigonometry134

hypotenusetheorem of Pythagoras

c a b

a bc

exact values surds

ac

b

bcaArea a2

Area c2

Area b2

Key

idea

s

Example 1 Finding the length of the hypotenuse

ba

5

12

c b

7

9.5

c

SOLUTION EXPLANATION

a c a b

c

c c

b c a b

c

a b

ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press

Measurement and Geometry 135

Example 2 Finding the length of the hypotenuse using exact values

SOLUTION EXPLANATION

c a b

c

c

2

5

c

1 ca 15

178

b 48

1450

c 2 2

2 z x y

a b

a c

b y

zx

c j

l

k

3 g ha b c d

e f g h

Exercise 3A

Unde

rsta

ndin

gFl

uenc

y

4 a

8

6c b 12

5c

c

15

8c

d 12

9 c

e 24

7c

f

409

c

g 48

14

c

h

18

24

c

i

15

20

c

Example 1a

ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press