1. a right-angled triangle
Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
two sides are given and you will work out one length
a scalene triangle
a right-angled triangle
Question
What is the length of a side for each of the squares below?
Area = 85cm2
Area = 36cm2
16cm2

2. a c c a b b a b c c b a a b c b c a hypotenuse
Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
hypotenuse
right-angle
opposite
longest length a c c a b b a b c
hypotenuse c b a a b c b c a

4. Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
Interesting fact: The iPad has a 25cm screen, this means that it’s diagonal length is 25cm. For all screens like computers, iPads, televisions, iPhones etc. the length quoted is always the diagonal length as this is always the longest.

5. Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
169 25
144

6. Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
8cm
15cm
5cm
12cm
7cm
15cm

7. 9cm 15cm ???cm 5cm 12cm ???cm ???cm ???cm 12cm 5cm 15cm 9cm
Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
???cm
???cm
12cm
5cm
9cm
15cm
5cm
9cm
???cm
15cm
12cm
???cm

8. Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
Imagine the squares
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12cm
5cm 52 x2
122
12cm
5cm
???cm
5cm
12cm
Write down your calculation x2
+ 52
= 122
Then take square roots to give the value of x
Look at your calculation and work through it
x = √119 x2
+ 25
= 144
= 144−25
= 119
x = cm x2

9. Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
Example 1 Work out the height of the trapezium, can you work out the area?
5.7cm
5.5cm
2.8cm
why?
5.5cm
2.9cm
2.9cm

10. Example 2 Work out the distance between the points (1,1) and (14,6)
Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
Example 2 Work out the distance between the points (1,1) and (14,6)

11. 5 3 4 The regulation for safe use of ladders states that:
Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem
Functional Maths
Pythagoras is used in real life and even as far back as Egyptian times (before Pythagoras), labourers used a trick to create a right angle.
The regulation for safe use of ladders states that:
the foot of a 6 m ladder must be placed between 1.3 m and 2.2 m from the foot of the wall.
What is the maximum height the ladder can safely reach up the wall? 5 3 4
To make a right-angle, which was needed to construct Pyramids Egyptians used a rope divided in the ratio 3:4:5 which made a right-angle when tied around three posts.