13-Jun-14Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem Finding the length of the smaller side Length of line using Pythagoras Theorem S4 Solving Real – Life Problems

S4 Starter Questions S4 ALWAYS comes up in exam !!

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Length of the smaller side Learning Intention Success Criteria 1.Use Pythagoras Theorem to find the length of smaller side. 1.To show how Pythagoras Theorem can be used to find the length of the smaller side. 2.Show all working. S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Pythagoras Revisited Two key points when dealing with right-angled triangles The longest side in a right-angled triangle is called The HYPOTENUSE The HYPOTENUSE is ALWAYS opposite the right angle a b c c 2 = a 2 + b 2 y x z (xz) 2 = (xy) 2 + (yz) 2 S4

13-Jun-14 Compiled by Mr. Lafferty Maths Dept. Calculating the Hypotenuse 8 12 c Q2.Calculate the longest length of the right- angled triangle below. Example 1

13-Jun-14 Compiled by Mr. Lafferty Maths Dept. Calculating the Hypotenuse Aeroplane b = 8 a = 15 c Lennoxtown Airport Q1.An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present which is 15km from the airport. It is at a height of 8km. How far away is the plane from the airport? Example 2

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Now try the Review on page 52 Calculating Hypotenuse

S4 S4 Starter Questions To get money from a cash machine, you need an appropriate card and a four-digit Personal Identification Number (PIN). Gary knows: His PIN contains the digits 2, 5, 6 and 9 2 is the first digit One possible PIN is shown in the table. Copy and complete the table with all possible PINs.

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Example :Find the length of side a ? Length of the smaller side To find the length of the smaller side of a right-angled triangle we simply rearrange Pythagoras Theorem. 20cm 12cm a cm Check answer ! Always smaller than hypotenuse S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Example :Find the length of side b ? Length of the smaller side 10cm b cm 8 cm Check answer ! Always smaller than hypotenuse S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Now try Ch5 Ex1 (Page 54) Length of smaller side S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Apply Pythagoras Theorem to find length of a line. 1.To show how Pythagoras Theorem can be used to find the length of a line. 2.Show all working. S4 Finding the Finding the Length of a Line

13-Jun-14 Created by Mr. Lafferty Maths Dept (7,7) (2,4) 3 5 Finding the Length of a Line Using the coordinate grid, can you draw a right-angled triangle containing the line we want to find the length of?.

13-Jun-14 Created by Mr. Lafferty Maths Dept (9,1) (0,6) 5 9 Pythagoras Theorem to find the length of a Line

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Now try Ex 2 Ch5 (page 56) Pythagoras Theorem to find the length of a Line S4

S4 Starter Questions 13-Jun-14Compiled by Mr. Lafferty Maths Dept. S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Solving Real – Life Problems Using Pythagoras Theorem Learning Intention Success Criteria 1.Apply Pythagoras Theorem to solve real-life problems. 1.To show how Pythagoras Theorem can be used to solve real-life problems. 2.Show all working. S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Example :A steel rod is used to support a tree which is in danger of falling down. What is the height of the tree ? Solving Real-Life Problems When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras Theorem to calculate its length. 17m 8m rod b a c S4

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Solving Real-Life Problems Example 2 A garden has a fence around its perimeter and along its diagonal as shown below. What is the length of the fence from D to C. 5m b m 13m AB CD S4

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13-Jun-14Compiled by Mr. Lafferty Maths Dept. Now try Ex 3 Ch5 (page 58) Mixed Examples S4