13-Jun-14Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem Finding the length of the smaller side Length of line using Pythagoras.

11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

Pythagoras Pythagoras TheoremTheorem

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Finding the length of the smaller side

Length of line using Pythagoras Theorem

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Solving Real – Life Problems

S4 Starter QuestionsS4 Starter Questionsw

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ALWAYS comes up in

exam !!


Length of the smaller Length of the smaller sideside

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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.

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Pythagoras Pythagoras RevisitedRevisited

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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

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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

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Example 1

11 Apr 2023Compiled by Mr. Lafferty Maths

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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

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Example 2


Now try the Reviewon page 52

Calculating Calculating HypotenuseHypotenuse

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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.


Example : Find the length of side a ?


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

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20cm 12cm

a cm

2 2 2a =c - bCheck answer ! Always smaller

than hypotenus

e

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Example : Find the length of side b ?


2 2 2c =a +b

2 2 2b =10 - 82b =36

b = 36 =6cm

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10cm b cm

8 cm

2 2 2b =c - a

Check answer ! Always smaller

than hypotenus

e

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Now tryCh5 Ex1 (Page 54)

Length of smaller Length of smaller sideside

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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

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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.


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Finding the Finding the Length of a LineLength of a Line

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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

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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


Now try Ex 2Ch5 (page 56)

Pythagoras Theorem Pythagoras Theorem to find the length of a to find the length of a

LineLine

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S4 Starter QuestionsS4 Starter Questions

11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

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Solving Real – Life Solving Real – Life ProblemsProblems

Using Pythagoras Using Pythagoras TheoremTheorem

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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.


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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

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17m

8m

rod

b

ac

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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

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5m

b m

13m

A B

CD

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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


Now try Ex 3Ch5 (page 58)

Mixed ExamplesMixed Examples

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13-Jun-14Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem Finding the length of the smaller side Length of line using Pythagoras.

Documents

lafferty maths

hypotenuse s4 slide

c s4 slide

pythagoras theorem s4

length of smaller

line slide

length of line

c slide