1. Starter Write down a definition of the hypotenuse
Find the hypotenuse of the following triangles:
2cm
9cm
15cm
8cm
11cm
6cm

2. Pythagoras’ Theorem
Learning Objectives: Be able to find the hypotenuse using Pythagoras Be able to find the shorter side using Be able to apply your knowledge to worded problems

3. Pythagoras’ Theorem c2 = a2 + b2 Square both the non-hypotenuse sides
Add the results together
Square root your answer to find the length of the hypotenuse

4. Pythagoras’ Theorem
c2 = a2 + b2 c2 = c2 = c2 = 65 c =√65 c = 8.1 4 C 7

5. Pythagoras’ Theorem
We can use Pythagoras’ theorem to find the a shorter side by re-arranging the formula.
c2 = a2 + b2
a2 = c2 – b2

6. Pythagoras’ Theorem
a2 = c2 – b2 a2 = 132 – 122 a2 = 169 – 144 a2 = 25 a = √25 a = 5
13cm
12cm a

7. Pythagoras’ Theorem 6cm b 14cm
a2 = c2 – b2 a2 = 142 – 62 a2 = 196 – 36 a2 = 160 a = √160 a = 12.65
6cm b
14cm

8. Pythagoras’ Theorem
Find the length of the missing side 3m
25m

9. Pythagoras’ Theorem
6cm
8.5cm

10. Starter Find the length of the missing side.
6cm
15cm
A ladder is leaning against a wall. It reaches 9m up the wall, and is 12m long. How far from the wall is the ladder standing?

11. Practical Problems
When using Pythagoras’ theorem to solve practical problems, draw a right-angled triangle to represent the problem
Identify the unknown variable by reading what the questions is asking
Identifying the known values and substitute these into Pythagoras’ theorem
Solve for the unknown value
Use the result to write the answer as a complete sentence

12. Pythagoras’ Theorem
A ladder is leaning against a wall. It reaches 9m up the wall, and is 12m long. How far from the wall is the ladder standing?

13. P

14. Pythagoras’ Theorem
A plane flies 120km due north, and then heads due east for 80km. How far is the plane from it’s starting point?
80km
c2 = a2 + b2
c2 =
c2 =
c2 = 20800
c = √20800
c = km (2dp)
120km

15. Pythagoras’ Theorem
The size of TV screens are measured by the diagonal distance from corner to corner. A 46” screen has a height of 30”. How wide is the screen?

16. Have I Got Hypotenuse For You
Rules:
Select a number
Answer the question – find the length of the hypotenuse
You have 1 minute
If you get it wrong, it passes over to the other team

17. The diagram shows a trapezium ABCD . Calculate the length of AB.
6.71cm 1
5cm
This rectangle has a diagonal of 13cm and a width of 12cm. Calculate it’s height. 2
12.73m 3 A
8cm C c 9m
13cm
7cm j B D 9m
10cm
12cm
Cardiff is 130 miles west of London. Hull is 200 miles north east of Cardiff. How far is Hull from London?
miles 4
8.54m 5
16.52cm 6
Hull 8m d
23cm
200 miles
16cm
Cardiff
London 3m
130 miles f
13.23cm 7
8.94cm 8
6.93m 9 b k
20cm a 4m
8cm 8m
12cm
15cm

18. CHECK YOUR ANSWERS AS YOU GO:
Your turn…
CHECK YOUR ANSWERS AS YOU GO:
Page 598
Exercise 26B, pages
Q1, 2 (shorter sides)
Exercise 26C, pages 555 – 557
Odd questions (worded problems)
Exam Questions, pages 558 – 599
Q4 – 8 (mixed, past exam questions)