1 / 14

Pythagoras’ Theorem

Pythagoras’ Theorem. Finding the hypotenuse. Pythagoras’ Theorem. The Hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle. Hypotenuse. Hypotenuse. Hypotenuse. Pythagoras’ Theorem – Finding the hypotenuse.

henrywood
Download Presentation

Pythagoras’ Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pythagoras’ Theorem A. Gilleran Finding the hypotenuse

  2. Pythagoras’ Theorem The Hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle Hypotenuse Hypotenuse Hypotenuse

  3. Pythagoras’ Theorem – Finding the hypotenuse Pythagoras’ Theorem allows us to find the length of any side in a right-angled triangle when we know the lengths of 2 sides a2 + b2 = c2 C is always the hypotenuse + 62 82 = c2 c a 64 + 36 = c2 8 100 = c2 = c b 6 = c

  4. Pythagoras’ Theorem – Finding the hypotenuse a2 + b2 = c2 C is always the hypotenuse + 62 42 = c2 c 16 + 36 = c2 52 = c2 a 4 = c b 6 = c

  5. Pythagoras’ Theorem – Finding the hypotenuse

  6. Pythagoras’ Theorem – Finding the hypotenuse x = 10.30cm (2dp) x = 5.92cm (2dp) x = 8.49cm (2dp) x = 20.62cm (2dp)

  7. Pythagoras’ Theorem A. Gilleran Finding the shorter side

  8. Pythagoras’ Theorem – Finding a shorter side We can rearrange Pythagoras’ equation to find the length of the shorter side when necessary We are trying to find the length of a. We need to rearrange our equation so that a is the subject a2 + b2 = c2 c 5 b 3 - b2 - b2 a2 = c2 – b2 x a

  9. Pythagoras’ Theorem – Finding a shorter side We can rearrange Pythagoras’ equation to find the length of the shorter side when necessary a2 = c2 - b2 a2 = 52 - 32 c 5 a2 = 25 - 9 b 3 a2 = 16 a = x a a =

  10. Pythagoras’ Theorem – Finding a shorter side

  11. Pythagoras’ Theorem – Finding a shorter side x = 14.66cm (2dp) x = 15cm x = 18.33cm (2dp) x = 6.33cm (2dp)

  12. Pythagoras’ Theorem – Stretch and Challenge A plane leaves Manchester airport heading due east. It flies 160 km before turning due north. It then flies a further 280 km and lands. What is the distance of the return flight if the plane flies straight back to Manchester airport? a2 + b2 = c2 +2802 1602 = c2 c 280km 25600 + 78400 = c2 b 104000 = c2 = c 160km = c a Manchester

  13. Pythagoras’ Theorem – Stretch and Challenge

  14. Pythagoras’ Theorem – Stretch and Challenge x = 6.63m x = 2.06m a) 127m b) 99.62m c) 27.38m

More Related