Pythagoras Theorem for Finding Hypotenuse and Shorter Side

Discover the essence of Pythagoras Theorem, particularly in finding the hypotenuse and shorter side of a right-angled triangle. Gain insight into the fundamentals and applications of this fundamental mathematical principle through clear examples and visual representations.

• Pythagoras Theorem
• Hypotenuse
• Right-angled Triangle
• Mathematics
• Theorem

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Uploaded on Sep 16, 2024 | 0 Views

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Presentation Transcript

1. Pythagoras Theorem 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

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 82+ 62= c2 64 + 36 = c2 100 = c2 ??? = c ?? = c c a 8 b 6

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

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 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 a x

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 a2 = 25 - 9 a2 = 16 a = ?? a = ? c 5 b 3 a x

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 1602+2802= c2 c 280km b 25600 + 78400 = c2 104000 = c2 ?????? = c 160km a ???.?? = c 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