1. Sides in a right angled triangle
Pythagoras’ result
Sides in a right angled triangle

6. The result: long side
H2 = A2 + B2 H A B

7. The result: long side H2 = A2 + B2
To find the length of the long side: H A B

8. The result: long side H2 = A2 + B2
To find the length of the long side: H A
Find the squares of the two shortest sides, add the result, take the square root of the total… B

9. Example: long side H2 = A2 + B2 To find the length of the long side: ?
12 cm
8 cm

10. Example: long side H2 = A2 + B2 To find the length of the long side: ?
12 cm
122 = 144
Square short sides
82 = 64
8 cm

11. Example: long side H2 = A2 + B2 To find the length of the long side: ?
12 cm
122 = 144
Square short sides
82 = 64
= 208
Add
8 cm

12. Example: long side H2 = A2 + B2 To find the length of the long side: ?
12 cm
122 = 144
Square short sides
82 = 64
= 208
Add
8 cm
√208 = 14.4
Square root

13. Your turn A. B. ? 10cm ? 10cm 8 cm 100 cm C. D. 13cm 18 cm 5cm ?
Is this triangle right angled?

14. Your turn: Answers A. B. 12.8 10cm 100.5 10cm 8 cm 100 cm C. D. 13cm
19.0
No, but close
14.1 cm
12 cm
Is this triangle right angled?

15. The result: short side A2 = H2 - B2
To find the length of the short side: H A B

16. The result: short side A2 = H2 - B2
To find the length of the short side: H A
Find the squares of the long side and the other short side, find the difference, take the square root of the total… B

17. Example: short side
A2 = H2 - B2
10 cm ?
7 cm

18. Example: short side A2 = H2 - B2 To find the length of the short side:
10 cm ?
7 cm

19. Example: short side A2 = H2 - B2 To find the length of the short side:
10 cm ?
102 = 100
Square known sides
72 = 49
7 cm

20. Example: short side A2 = H2 - B2 To find the length of the short side:
10 cm ?
102 = 100
Square known sides
72 = 49
= 51
Subtract
7 cm

21. Example: short side A2 = H2 - B2 To find the length of the short side:
10 cm ?
102 = 100
Square known sides
72 = 49
= 51
Subtract
7 cm
√51 = 7.14 cm
Square root

22. Your turn A. B. 13cm 8cm 75cm 15cm ? ? C. D. 20cm ? 12cm
Diagonal is 14.1 cm long
How long is side?

23. Your turn: answers A. B. 13cm 8cm 75cm 15cm 73.5cm 10.2cm C. D. 20cm
Diagonal is 14.1 cm long
How long is side?

24. Mixed problems

25. Mixed problems
Find the right angle

26. Mixed problems
Find the right angle
Opposite side is always longest

27. Mixed problems Find the right angle Opposite side is always longest
If you know both short sides: square and add

28. Mixed problems Find the right angle Opposite side is always longest
If you know both short sides: square and add
If you know a long and a short side: square and subtract

29. Mixed problems Find the right angle Opposite side is always longest
If you know both short sides: square and add
If you know a long and a short side: square and subtract
Take square root at the end…

30. Example A ladder leans against a wall.
The ladder is 15ft long, and the foot of the ladder is placed 3 ft away from the wall.
How high up the wall does the ladder reach?

31. Example
Right angle is assumed to be between wall and ground!

32. Example Right angle is assumed to be between wall and ground!
The 15ft ladder is the longest side

33. Example Right angle is assumed to be between wall and ground!
The 15ft ladder is the longest side
15ft ?
The height up the wall is the missing short side
3ft

34. Example Right angle is assumed to be between wall and ground!
The 15ft ladder is the longest side
15ft ?
The height up the wall is the missing short side
= = 216
3ft

35. Example Right angle is assumed to be between wall and ground!
The 15ft ladder is the longest side
15ft ?
The height up the wall is the missing short side
= = 216
3ft
√216 = 14.7 ft

36. Your turn Find the mixed exercises in your textbook
Make sure you know where the right angle is
Check that your answers make sense (the longest side must always be less than the sum of the two short sides!)