1. Starter Jane is 40. Chris is 10. Chris is ¼ of Jane’s age.
In 5 years time, Jane is 45, Chris is 15. Chris is 1/3 of Jane’s age.
In another 15 years time, Jane is 60, Chris is 30. He’s now only ½ her age.
At what point will Chris overtake Jane?

2. Pythagoras’ Theorem
Learning Objectives: Be able to label a right angled triangle Be able to use Pythagoras to find the hypotenuse Able to apply to worded problems

3. Pythagoras’ Theorem
KEY WORDS: Hypotenuse: The longest side on a right angled triangle Right Angled Triangle: is classified by the type of angle it contains.

4. Pythagoras’ Theorem
For any right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two shorter sides.
Builders use Pythagoras’ theorem for building frames and walls

5. Pythagoras’ Theorem Which of these sides is the hypotenuse? cb c
hypotenuse b a b a a
Which of these sides is the hypotenuse?

6. Finding the Length of the Hypotenuse
To calculate the length of the hypotenuse, you must be given the length of the two shorter sides a and b, substitute the values of a and b into the rule c2 = a2 +b2 and solve for c
REMEMBER that the hypotenuse is the longest side, so the value of c must be greater than a or b

7. Pythagoras’ Theorem Find the length of the hypotenuse. c2 = a2 + b2
c = 27.46cm c
15cm
23cm

8. Pythagoras’ Theorem
Find the hypotenuse of the following triangle. Round your answer to 2dp.
c2 = a2 + b2
c2 =
c2 =
c2 = 185
c = √185
c = 13.60cm
11cm
8cm c

10. Which of the sides in these triangles is the hypotenuse?b b
Calculate the length of c. c
5cm
12cm

11. Pythagoras’ Theorem
Learning Objectives: Be able to label a right angled triangle Be able to use Pythagoras to find the hypotenuse Able to apply to worded problems

12. Exit Ticket
In your books, find the hypotenuse of the following. Round your answers to 2dp where necessary. c
18cm 4m

13. Exit ticket
In your books, find the hypotenuse of the following. Round your answers to 2dp where necessary.
13cm c
10cm

14. Pythagoras’ Theorem
Exercise 26A, pages 551 – 552 Q1 – 9 Sketch the triangles and show your working out

15. Plenary
A plane flies due north for 180km, then due west for 260km. How far is the plane from it’s starting position?
Draw and label a triangle to represent the situation
Write out the formula you’d use to answer the question
Find the distance