1. Using Pythagoras’ Theorem
L.O.
Use Pythagoras Theorem to find missing sides on a triangle
Solve real-life problems using Pythagoras Theorem
We are learning this because…
3000 years ago the Egyptians used Pythagoras Theorem to build the Great Pyramids using knotted rope to make a 90o angle using a 3,4,5 triangle. Today builders using pieces of wood with length 3ft, 4ft, 5ft to the same thing to get a perfect 90o right angle
Level 7
Level 8

2. Pythagoras’ Theorem
I was born at Samos, in Greece, and lived from 580 to 500 B.C.
I was a Mathematician who became famous for discovering something unique about right – angled triangles.
Now you are going to try to find out what I discovered!!

3. Using Pythagoras’ Theorem
Area C c2
So what is Pythagoras’ Theorem?
He said that:
Area A a2 a b c
a2 + b2 = c2
Area B b2
“For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.”
Pythagoras

4. Using Pythagoras’ Theorem
We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle
Area C
9 +16 = 25
Find the Length of side x
Area A
32 = 9
We SQUARE to get the area of the smaller squares x
3cm
How do we get the length of side x
x =25 = 5cm
4cm
We ADD to get the area of the biggest square
Area B
42 = 16
We SQUARE ROOT the area to get the length of side x

5. Using Pythagoras’ Theorem
Level 7
We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle
Example 1
Find the Length of side x
Square
92 = 81 x
72 = 49
7cm
Add
x2 = 130
9cm
Square x =  130
Root
x = 11.4cm

6. Using Pythagoras’ Theorem
Level 7
We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle
Example 2
Find the Length of side x
Square
82 = 64 x
42 = 16
4cm
Add
x2 = 80
8cm
Square x =  80
Root
x = 8.9

7. Using Pythagoras’ Theorem
Level 7
We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle
Example 3
Find the Length of side x
Square
122 = 144
12cm x
72 = 49
Subtract
x2 = 95
7cm
Square x =  95
Root
x = 9.7cm

8. Using Pythagoras’ Theorem
Level 7
We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle
Example 4
Find the Length of side x
Square
232 = 529
23mm
15mm
152 = 225
Subtract x
x2 = 304
Square x =  304
Root
x = 17.4cm

9. Using Pythagoras’ Theorem
For each of the following triangles, calculate the length of the missing side, giving your answers to one decimal place when needed.
19m
14m 1 2
5cm
11cm 3
3cm
6cm
Answer = 6.7cm
Answer = 9.8cm
Answer = 23.6m
1.5cm
1.1cm
25cm
60cm 4 5 6
12mm
13mm
Answer = 5mm
Answer = 1.0cm
Answer = 65cm
Level 7

10. Using Pythagoras’ Theorem7
Calculate the length of the diagonal of this square. 8
If a right angle has short lengths 14cm and 8cm, what is the length of the longest side.
6cm
Answer = 16.1cm
Answer = 8.5cm 9 10
Calculate the height of this isosceles triangle.
Calculate the base of this
isosceles triangle.
Answer = 12cm
Answer = 11.3cm
10cm
10cm
12cm
12cm
8cm
8cm

11. Pythagoras’ Theorem Answer = 75miles Answer = 27.7m Level 8
Real Life Problem 1
A boat travels 45 miles east then 60 miles north, how far is it from where it started? (hint: draw a diagram)
Answer = 75miles
Real Life Problem 2
A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they have swam? (hint: draw a diagram)
Answer = 27.7m

12. Pythagoras’ Theorem Answer = 3.7m Answer = 9.5m Level 8
Real Life Problem 3
A ladder which is 4m long leans against a wall, the bottom of the ladder is 1.5m from the bottom of the wall, how high up the wall does the ladder go? (hint: draw a diagram)
Answer = 3.7m
Real Life Problem 4
A rope of length 10m is stretched from the top of a pole 3m high until it reaches the ground. How far is the end of the rope to the base of the pole.(hint: draw a diagram)
Answer = 9.5m