Download presentation
Presentation is loading. Please wait.
1
Using Pythagoras’ Theorem
L.O. Use Pythagoras Theorem to find missing sides on a triangle Solve real-life problems using Pythagoras Theorem We are learning this because… 3000 years ago the Egyptians used Pythagoras Theorem to build the Great Pyramids using knotted rope to make a 90o angle using a 3,4,5 triangle. Today builders using pieces of wood with length 3ft, 4ft, 5ft to the same thing to get a perfect 90o right angle Level 7 Level 8
2
Pythagoras’ Theorem I was born at Samos, in Greece, and lived from 580 to 500 B.C. I was a Mathematician who became famous for discovering something unique about right – angled triangles. Now you are going to try to find out what I discovered!!
3
Using Pythagoras’ Theorem
Area C c2 So what is Pythagoras’ Theorem? He said that: Area A a2 a b c a2 + b2 = c2 Area B b2 “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” Pythagoras
4
Using Pythagoras’ Theorem
We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle Area C 9 +16 = 25 Find the Length of side x Area A 32 = 9 We SQUARE to get the area of the smaller squares x 3cm How do we get the length of side x x =25 = 5cm 4cm We ADD to get the area of the biggest square Area B 42 = 16 We SQUARE ROOT the area to get the length of side x
5
Using Pythagoras’ Theorem
Level 7 We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle Example 1 Find the Length of side x Square 92 = 81 x 72 = 49 7cm Add x2 = 130 9cm Square x = 130 Root x = 11.4cm
6
Using Pythagoras’ Theorem
Level 7 We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle Example 2 Find the Length of side x Square 82 = 64 x 42 = 16 4cm Add x2 = 80 8cm Square x = 80 Root x = 8.9
7
Using Pythagoras’ Theorem
Level 7 We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle Example 3 Find the Length of side x Square 122 = 144 12cm x 72 = 49 Subtract x2 = 95 7cm Square x = 95 Root x = 9.7cm
8
Using Pythagoras’ Theorem
Level 7 We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle Example 4 Find the Length of side x Square 232 = 529 23mm 15mm 152 = 225 Subtract x x2 = 304 Square x = 304 Root x = 17.4cm
9
Using Pythagoras’ Theorem
For each of the following triangles, calculate the length of the missing side, giving your answers to one decimal place when needed. 19m 14m 1 2 5cm 11cm 3 3cm 6cm Answer = 6.7cm Answer = 9.8cm Answer = 23.6m 1.5cm 1.1cm 25cm 60cm 4 5 6 12mm 13mm Answer = 5mm Answer = 1.0cm Answer = 65cm Level 7
10
Using Pythagoras’ Theorem
7 Calculate the length of the diagonal of this square. 8 If a right angle has short lengths 14cm and 8cm, what is the length of the longest side. 6cm Answer = 16.1cm Answer = 8.5cm 9 10 Calculate the height of this isosceles triangle. Calculate the base of this isosceles triangle. Answer = 12cm Answer = 11.3cm 10cm 10cm 12cm 12cm 8cm 8cm
11
Pythagoras’ Theorem Answer = 75miles Answer = 27.7m Level 8
Real Life Problem 1 A boat travels 45 miles east then 60 miles north, how far is it from where it started? (hint: draw a diagram) Answer = 75miles Real Life Problem 2 A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they have swam? (hint: draw a diagram) Answer = 27.7m
12
Pythagoras’ Theorem Answer = 3.7m Answer = 9.5m Level 8
Real Life Problem 3 A ladder which is 4m long leans against a wall, the bottom of the ladder is 1.5m from the bottom of the wall, how high up the wall does the ladder go? (hint: draw a diagram) Answer = 3.7m Real Life Problem 4 A rope of length 10m is stretched from the top of a pole 3m high until it reaches the ground. How far is the end of the rope to the base of the pole.(hint: draw a diagram) Answer = 9.5m
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.