Starter

a) Write down a definition of the hypotenuse

b) Find the hypotenuse of the following triangles:

8cm

6cm

15cm

2cm9cm

11cm

Pythagoras’ Theorem

Learning Objectives:

Be able to find the hypotenuse using Pythagoras Be able to find the shorter side using Pythagoras Be able to apply your knowledge to worded problems

Pythagoras’ Theorem

• c2 = a2 + b2

1.Square both the non-hypotenuse sides2.Add the results together3.Square root your answer to find the length of

the hypotenuse

Pythagoras’ Theorem

c2 = a2 + b2

c2 = 42 + 72

c2 = 16 + 49c2 = 65c =√65c = 8.14

7

C

Pythagoras’ Theorem

• We can use Pythagoras’ theorem to find the a shorter side by re-arranging the formula.

• c2 = a2 + b2

• a2 = c2 – b2

Pythagoras’ Theorem

a2 = c2 – b2

a2 = 132 – 122

a2 = 169 – 144a2 = 25a = √25a = 5

12cm

a

13cm

Pythagoras’ Theorem

a2 = c2 – b2

a2 = 142 – 62

a2 = 196 – 36a2 = 160a = √160a = 12.65

6cm

14cm b

Pythagoras’ Theorem

• Find the length of the missing side

3m25m

Pythagoras’ Theorem

8.5cm

6cm

Starter• Find the length of the missing side.

6cm15cm

2m

24m

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?

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

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?

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?

120km

80kmc2 = a2 + b2

c2 = 1202 + 802

c2 = 14400 + 6400c2 = 20800c = √20800c = 144.22km (2dp)

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?

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

6.71cm

16.52cm8.54m151.99 miles

12.73m5cm

6.93m8.94cm13.23cm

The diagram shows a trapezium ABCD . Calculate the length of AB.

Cardiff is 130 miles west of London. Hull is 200 miles north east of Cardiff.

How far is Hull from London?

This rectangle has a diagonal of 13cm and a width of 12cm.

Calculate it’s height.

12cm 8cm

b

3m

8m d

9m

9m

23cm16cm

f

c

k

4m8m

15cm

a

10cm

7cm

8cmA

D

C

B

20cm

130 miles

200 miles

Cardiff London

Hull

j

12cm

13cm

65

3

98

1 2

4

7

Your turn…

• Exercise 26B, pages 553-554 – Q1, 2 (shorter sides)

• Exercise 26C, pages 555 – 557 – Odd questions (worded problems)

• Exam Questions, pages 558 – 599– Q4 – 8 (mixed, past exam questions)

CHECK YOUR ANSWERS AS

YOU GO:Page 598