year 8 maths

178 Chapter 3 Measurement and Pythagoras’ theorem
Example 25
Finding the length of the hypotenuse
Find the length of the hypotenuse for these right-angled triangles. Round the answer for part b to
two decimal places.
a
b
9
c
6
c
8
7
SOLUTION
a c 2 = a 2 + b 2
= 6 2 + 8 2
= 100
∴ c = √100
= 10
b c 2 = a 2 + b 2
= 7 2 + 9 2
= 130
∴ c = √130
= 11.40 (to 2 d.p.)
EXPLANATION
Write the equation for Pythagoras’ theorem and
substitute the values for the shorter sides.
Find c by taking the square root.
First calculate the value of 7 2 + 9 2 .
√130 is a surd, so round the answer as required.
Example 26
Applying Pythagoras’ theorem
A rectangular wall is to be strengthened by a diagonal brace. The wall is 6 m wide and 3 m high. Find
the length of brace required, correct to the nearest cm .
Brace
3 m
6 m
SOLUTION
c 2 = a 2 + b 2
= 3 2 + 6 2
= 45
c = √45
= 6.71 m or 671 cm (nearest cm)
EXPLANATION
c a = 3
b = 6
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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