1. Finding the hypotenuse
Pythagoras’ Theorem
A. Gilleran
Finding the hypotenuse

2. Pythagoras’ Theorem
The Hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle
Hypotenuse
Hypotenuse
Hypotenuse

3. Pythagoras’ Theorem – Finding the hypotenuse
Pythagoras’ Theorem allows us to find the length of any side in a right-angled triangle when we know the lengths of 2 sides
a2 + b2 = c2
C is always the hypotenuse 82
+ 62
= c2 c
= c2 a 8
100 = c2
𝟏𝟎𝟎 = c b 6
𝟏𝟎 = c

4. Pythagoras’ Theorem – Finding the hypotenuse
a2 + b2 = c2
C is always the hypotenuse 42
+ 62
= c2 c
= c2
52 = c2 a 4 b
𝟓𝟐 = c 6
𝟕𝟐 = c

5. Pythagoras’ Theorem – Finding the hypotenuse

6. Pythagoras’ Theorem – Finding the hypotenuse
x = 10.30cm (2dp)
x = 5.92cm (2dp)
x = 8.49cm (2dp)
x = 20.62cm (2dp)

7. Finding the shorter side
Pythagoras’ Theorem
A. Gilleran
Finding the shorter side

8. Pythagoras’ Theorem – Finding a shorter side
We can rearrange Pythagoras’ equation to find the length of the shorter side when necessary
We are trying to find the length of a.
We need to rearrange our equation so that a is the subject
a2 + b2 = c2 5 c b 3
- b2
- b2
a2 = c2 – b2 x a

9. Pythagoras’ Theorem – Finding a shorter side
We can rearrange Pythagoras’ equation to find the length of the shorter side when necessary
a2 = c2 - b2
a2 = 52
- 32 5 c
a2 = b 3
a2 = 16
a = 𝟏𝟔 x a
a = 𝟒

10. Pythagoras’ Theorem – Finding a shorter side

11. Pythagoras’ Theorem – Finding a shorter side
x = 15cm
x = 14.66cm (2dp)
x = 6.33cm (2dp)
x = 18.33cm (2dp)

12. Pythagoras’ Theorem – Stretch and Challenge
A plane leaves Manchester airport heading due east. It flies 160 km before turning due north.
It then flies a further 280 km and lands. What is the distance of the return flight if the plane
flies straight back to Manchester airport?
a2 + b2 = c2
1602
+2802
= c2 c
280km
= c2 b
= c2
𝟏𝟎𝟒𝟎𝟎𝟎 = c
160km a
𝟑𝟐𝟐.𝟒𝟗 = c
Manchester

13. Pythagoras’ Theorem – Stretch and Challenge

14. Pythagoras’ Theorem – Stretch and Challenge
x = 6.63m
x = 2.06m
a) 127m
b) 99.62m
c) 27.38m