Starter Jane is 40. Chris is 10. Chris is ¼ of Jane’s age.

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Presentation transcript:

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? http://www.youtube.com/watch?v=4xpTjMhdIA0

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

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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

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

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

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

Pythagoras’ Theorem Find the hypotenuse of the following triangle. Round your answer to 2dp. c2 = a2 + b2 c2 = 82 + 112 c2 = 64 + 121 c2 = 185 c = √185 c = 13.60cm 11cm 8cm c

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

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

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

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

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

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