year 8 maths

3M
Calculating the length of a shorter side
181
3M Calculating the length of a shorter side
We know that if we are given the two shorter sides of a right-angled triangle we can use Pythagoras’
theorem to find the length of the hypotenuse. Generalising further, we can say that when given any two
sides of a right-angled triangle we can use Pythagoras’ theorem to find the length of the third side.
L et’s start: What’s the setting out?
The triangle shown has a hypotenuse length of 15 and one of the shorter sides is of length 12 . Here is the
setting out to find the length of the unknown side a .
Can you fill in the missing gaps and explain what is happening at each step.
a 2 + b 2 = c 2
a 2 + ___ 2 = ___ 2
a 2 + ___ = ___
a 2 = ___ (Subtract ___ from both sides.)
∴ a = √_________
= ___
12
a
15
(Hypotenuse)
■ Pythagoras’ theorem can be used to find the length of the shorter sides of a right-angled
triangle if the length of the hypotenuse and another side are known.
■ Use subtraction to make the unknown the subject of the equation.
For example:
a 2 + b 2 = c 2
a 2 + 24 2 = 25 2
a 2 + 576 = 625
a
a 2 = 49 (Subtract 576 from both sides.)
∴ a = √49
= 7
25
24
Key ideas
Example 27
Finding the length of a shorter side
Find the value of a in this right-angled triangle.
5
a
SOLUTION
a 2 + b 2 = c 2
a 2 + 4 2 = 5 2
a 2 + 16 = 25
a 2 = 9
∴ a = √9
= 3
EXPLANATION
Write the equation for Pythagoras’ theorem and
substitute the known values.
Subtract 16 from both sides.
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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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