Cambridge International Mathematics

172 The theorem of Pythagoras (Chapter 8)

Example 3 Self Tutor

Findxin surd form:

ab

a The hypotenuse has lengthxcm.

) x^2 =2^2 +(

p

10)^2 fPythagorasg

) x^2 =4+10

) x^2 =14

) x=

p

14 fas x> 0 g

b (2x)^2 =x^2 +6^2 fPythagorasg

) 4 x^2 =x^2 +36

) 3 x^2 =36

) x^2 =12

) x=

p

12 fas x> 0 g

) x=2

p

3

Example 4 Self Tutor

Find the value ofy, giving your answer

correct to 3 significant figures.

In triangle ABC, the hypotenuse isxcm.

) x^2 =5^2 +1^2 fPythagorasg

) x^2 =26

) x=

p

26 fas x> 0 g

In triangle ACD, the hypotenuse is 6 cm.

) y^2 +(

p

26)^2 =6^2 fPythagorasg

) y^2 +26=36

) y^2 =10

) y=

p

10 fas y> 0 g

) y¼ 3 : 16

EXERCISE 8A.1

1 Find the length of the hypotenuse in the following triangles, giving your answers correct to 3 significant

figures:

abc

Since we must find

the value of , we

leave in surd form.

Rounding it will

reduce the accuracy

of our value for.

y

x

y

2mx

xm

6m

5cm

1cm

6cm

ycm xcm

A B

D C

xcm 2cm

~` 1 ` 0 cm

4cm

7cm xcm

5cm

xcm 8km

13 km

xkm

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Y:\HAESE\IGCSE01\IG01_08\172IGCSE01_08.CDR Tuesday, 16 September 2008 10:35:24 AM PETER