year 8 maths

182 Chapter 3 Measurement and Pythagoras’ theorem
Example 28
Applying Pythagoras to find a shorter side
A 10 m steel brace holds up a concrete wall. The bottom of the
brace is 5 m from the base of the wall. Find the height of the
concrete wall, correct to two decimal places.
10 m
Wall
5 m
SOLUTION
Let a metres be the height of the wall.
a 2 + b 2 = c 2
a 2 + 5 2 = 10 2
a 2 + 25 = 100
a 2 = 75
a = √75
= 8.66 (to 2 d.p.)
The height of the wall is 8.66 metres.
EXPLANATION
Choose a letter (pronumeral) for the unknown height.
Substitute into Pythagoras’ theorem.
Subtract 25 from both sides.
√75 is the exact answer.
Round as required.
Answer a worded problem using a full sentence.
Exercise 3M
UNDERSTANDING AND FLUENCY
1–4 2, 3–4(½)
3–4(½)
1 Write Pythagoras’ theorem for each given triangle.
a
b 5
m 9
p
10
c
15
w d
w
c
12
8
3
2 Copy and complete the missing steps.
a
15
9
a
a 2 + b 2 = c 2
a 2 + 9 2 = ___
a 2 + ___ = 225
a 2 = ___
∴ a = √______
= ___
b
b
25
a 2 + b 2 = c 2
7 2 + b 2 = ____
___ + b 2 = ___
b 2 = 576
∴ b = √______
= ___
7
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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