11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Pythagoras Pythagoras TheoremTheorem
ww
w.m
ath
srevis
ion
.com
Finding the length of the smaller side
Length of line using Pythagoras Theorem
S4
Solving Real – Life Problems
S4 Starter QuestionsS4 Starter Questionsw
ww
.math
srevis
ion
.com
S4
ALWAYS comes up in
exam !!
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Length of the smaller Length of the smaller sideside
ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Use Pythagoras Use Pythagoras Theorem to find the Theorem to find the length of smaller side.length of smaller side.
1. To show how Pythagoras Theorem can be used to find the length of the smaller side.
2.2. Show all working.Show all working.
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Pythagoras Pythagoras RevisitedRevisited
ww
w.m
ath
srevis
ion
.com
Two key points when dealing with right-angled triangles
The longest side in a right-angled triangle is calledThe HYPOTENUSE
The HYPOTENUSE is ALWAYS opposite the right angle
a
b cc2 = a2 + b2
y
x
z
(xz)2 = (xy)2 + (yz)2
S4
11 Apr 2023Compiled by Mr. Lafferty Maths
Dept.
Calculating the HypotenuseCalculating the Hypotenuse
8
12
c
Q2. Calculate the longest length of the right-angled triangle below.
2 2 2c =a +b2 2 2c =12 +8
2c =208
c = 208 =14.42km
ww
w.m
ath
srevis
ion
.com
Example 1
11 Apr 2023Compiled by Mr. Lafferty Maths
Dept.
Calculating the Hypotenuse
Aeroplaneb = 8
a = 15
c
Lennoxtown
Airport
Q1.Q1. An aeroplane is preparing to land at Glasgow An aeroplane is preparing to land at Glasgow Airport. Airport. It is over Lennoxtown at present which is It is over Lennoxtown at present which is 15km from 15km from the airport. It is at a height of 8km. the airport. It is at a height of 8km.
How far away is the plane from the airport?How far away is the plane from the airport?
2 2 2c =a +b2 2 2c =15 +8
2c =289
c = 289 =17km
ww
w.m
ath
srevis
ion
.com
Example 2
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try the Reviewon page 52
Calculating Calculating HypotenuseHypotenuse
ww
w.m
ath
srevis
ion
.com
ww
w.m
ath
srevis
ion
.com
S4
S4 Starter Questions
To get money from a cash machine, you need an appropriate card and a four-digit Personal Identification Number (PIN).
Gary knows: His PIN contains the digits 2, 5, 6 and 9 2 is the first digit
One possible PIN is shown in the table.Copy and complete the table with all possible PINs.
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Example : Find the length of side a ?
Length of the smaller Length of the smaller sideside
To find the length of the smaller side of a right-angled triangle
we simply rearrange Pythagoras Theorem.
2 2 2c =a +b
2 2 2a =20 -122a =256
a= 256 =16cm
ww
w.m
ath
srevis
ion
.com
20cm 12cm
a cm
2 2 2a =c - bCheck answer ! Always smaller
than hypotenus
e
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Example : Find the length of side b ?
Length of the smaller Length of the smaller sideside
2 2 2c =a +b
2 2 2b =10 - 82b =36
b = 36 =6cm
ww
w.m
ath
srevis
ion
.com
10cm b cm
8 cm
2 2 2b =c - a
Check answer ! Always smaller
than hypotenus
e
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now tryCh5 Ex1 (Page 54)
Length of smaller Length of smaller sideside
ww
w.m
ath
srevis
ion
.com
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
S4 Starter QuestionsS4 Starter Questionsw
ww
.math
srevis
ion
.com
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Apply Pythagoras Theorem Apply Pythagoras Theorem to find length of a line.to find length of a line.
1. To show how Pythagoras Theorem can be used to find the length of a line.
2.2. Show all working.Show all working.
S4
Finding the Finding the Length of a LineLength of a Line
11 Apr 2023Created by Mr. Lafferty Maths
Dept.w
ww
.math
srevis
ion
.com
1 32 540
1
3
2
5
4
1 32 40
1
32
54
6
5 76 8 9 10
78
(7,7)
(2,4)
3
5
Finding the Length of a Line
Using the coordinate grid, can you draw a right-angled
triangle containing the line we want to find the length of?.
2 2 2c a b
2 2 25 3c
25 9c
34c
5.83c
11 Apr 2023Created by Mr. Lafferty Maths
Dept.w
ww
.math
srevis
ion
.com
1 32 540
1
3
2
5
4
1 32 40
1
32
54
6
5 76 8 9 10
78
(9,1)
(0,6)
5
9
2 2 2c a b
2 2 25 9c
25 81c
106c
10.3c
Pythagoras Theorem to find the length of a Line
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 2Ch5 (page 56)
Pythagoras Theorem Pythagoras Theorem to find the length of a to find the length of a
LineLine
ww
w.m
ath
srevis
ion
.com
S4
S4 Starter QuestionsS4 Starter Questions
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
w.m
ath
srevis
ion
.com
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Solving Real – Life Solving Real – Life ProblemsProblems
Using Pythagoras Using Pythagoras TheoremTheorem
ww
w.m
ath
srevis
ion
.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Apply Pythagoras Theorem Apply Pythagoras Theorem to solve real-life problems.to solve real-life problems.
1. To show how Pythagoras Theorem can be used to solve real-life problems.
2.2. Show all working.Show all working.
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Example : A steel rod is used to support a treewhich is in danger of falling down.
What is the height of the tree ?
Solving Real-Life Solving Real-Life ProblemsProblems
When coming across a problem involving When coming across a problem involving finding a missing side in a right-angled triangle, finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem you should consider using Pythagoras’ Theorem to calculate its length.to calculate its length.
2 2 2c a b
2 2 217 - 8a
2 225a
225 15a m
ww
w.m
ath
srevis
ion
.com
17m
8m
rod
b
ac
S4
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Solving Real-Life Solving Real-Life ProblemsProblems
Example 2Example 2A garden has a fence around its perimeter and A garden has a fence around its perimeter and along its diagonal as shown below. along its diagonal as shown below. What is the length of the fence from D to C.What is the length of the fence from D to C.
2 2 2( ) ( ) ( )AC DC AD
2 2 2( ) 13 - 5DC
2( ) 144DC
144 12DC m
ww
w.m
ath
srevis
ion
.com
5m
b m
13m
A B
CD
S4
A
B
C D E F
G H
IJ
K L
P(x,y)
o
r
M
N
O
P
Q R
S
T
U V
W Z
AC
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 3Ch5 (page 58)
Mixed ExamplesMixed Examples
ww
w.m
ath
srevis
ion
.com
S4