Finding the hypotenuse

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Presentation transcript:

Finding the hypotenuse Pythagoras’ Theorem A. Gilleran 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 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 c 64 + 36 = c2 a 8 100 = c2 𝟏𝟎𝟎 = c b 6 𝟏𝟎 = c

Pythagoras’ Theorem – Finding the hypotenuse a2 + b2 = c2 C is always the hypotenuse 42 + 62 = c2 c 16 + 36 = c2 52 = c2 a 4 b 𝟓𝟐 = c 6 𝟕𝟐 = c

Pythagoras’ Theorem – Finding the hypotenuse

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

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

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 5 c b 3 - b2 - b2 a2 = c2 – b2 x a

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 5 c a2 = 25 - 9 b 3 a2 = 16 a = 𝟏𝟔 x a a = 𝟒

Pythagoras’ Theorem – Finding a shorter side

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

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 25600 + 78400 = c2 b 104000 = c2 𝟏𝟎𝟒𝟎𝟎𝟎 = c 160km a 𝟑𝟐𝟐.𝟒𝟗 = c Manchester

Pythagoras’ Theorem – Stretch and Challenge

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