S4_General_Pythagoras_Revisited_TJ_Chapter5

# S4_General_Pythagoras_Revisited_TJ_Chapter5 - S4 Pythagoras...

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Unformatted text preview: S4 Pythagoras Theorem www.mathsrevision.com Finding the length of the smaller side Length of line using Pythagoras Theorem Solving Real Life Problems 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 ALWAYS comes up S4 Starter Questions in exam !! www.mathsrevision.com Length of the smaller side S4 Learning Intention Success Criteria 1. Use Pythagoras Theorem to find the length of smaller side. 2. Show all working. www.mathsrevision.com 1. To show how Pythagoras Theorem can be used to find the length of the smaller side. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Pythagoras Revisited S4 Two key points when dealing with rightangled triangles www.mathsrevision.com The longest side in a rightangled triangle is called The HYPOTENUSE The HYPOTENUSE is ALWAYS opposite the right angle b 13 Feb 2012 c a c2 = a2 + b2 (xz)2 = (xy)2 + (yz)2 x y z Compiled by Mr. Lafferty Maths Dept. Calculating the Hypotenuse Example 1 Q2. Calculate the longest length of the right below. angled triangle www.mathsrevision.com c 2 = a 2 +b 2 c 2 = 12 2 + 8 2 c2 =208 c = 2 0 8 = 14 .4 2 k m Compiled by Mr. Lafferty Maths Dept. c 12 8 13 Feb 2012 Calculating the Hypotenuse Example 2 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? www.mathsrevision.com c 2 = a 2 +b 2 c 2 = 15 2 + 8 2 c =289 2 c Airport a = 15 Aeroplane b = 8 Lennoxtown c = 2 8 9 = 17 k m 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Calculating Hypotenuse www.mathsrevision.com Now try the Review on page 52 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4 To get money from a cash machine, you need an appropriate card and a fourdigit 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. www.mathsrevision.com Length of the smaller side S4 www.mathsrevision.com To find the length of the smaller side of a rightangled triangle we simply rearrange Pythagoras Theorem. Example : Find the length of side a ? Check answer ! Always smaller than hypotenuse c 2 = a 2 +b 2 a2 = c 2 b 2 a 2 = 2 0 2 12 2 a2 = 2 5 6 a = 2 5 6 = 16 c m Compiled by Mr. Lafferty Maths Dept. 20cm a cm 12cm 13 Feb 2012 Length of the smaller side S4 www.mathsrevision.com Example : Find the length of side b ? c 2 = a 2 +b 2 b 2 = c 2 a2 b 2 = 10 2 8 2 b2 =36 10cm 8 cm b cm Check answer ! Always smaller than hypotenuse b = 36 =6cm Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Length of smaller side S4 www.mathsrevision.com Now try Ch5 Ex1 (Page 54) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Finding the Length of a Line Learning Intention Success Criteria 1. Apply Pythagoras Theorem to find length of a line. 2. Show all working. www.mathsrevision.com 1. To show how Pythagoras Theorem can be used to find the length of a line. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 5 48 www.mathsrevision.com Using the coordinate grid, can you draw a Finding the rightangled triangle containing the line we Length of a Line want to find the length of?. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 7 36 5 24 3 2 1 1 (7,7) 3 (2,4) 5 c2 = a 2 + b2 c =5 +3 2 2 2 c = 25 + 9 c = 34 c = 5.83 1 2 3 2 5 1 4 6 3 7 4 8 9 5 10 00 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 5 48 www.mathsrevision.com Pythagoras Theorem to find the length of a Line c2 = a 2 + b2 c =5 +9 2 2 2 7 (0,6) 36 5 24 5 3 2 1 1 c = 25 + 81 (9,1) 6 3 7 4 8 9 5 10 c = 106 9 c = 10.3 00 1 2 3 2 5 1 4 S4 Pythagoras Theorem to find the length of a Line www.m a th s re vis io n .c o m Now try Ex 2 Ch5 (page 56) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Solving Real Life Problems Using Pythagoras Theorem Learning Intention Success Criteria 1. Apply Pythagoras Theorem to solve reallife problems. 2. Show all working. www.m a th s re vis io n .c o m 1. To show how Pythagoras Theorem can be used to solve reallife problems. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Solving Real-Life Problems S4 www.mathsrevision.com When coming across a problem involving finding a missing side in a rightangled triangle, you should consider using Pythagoras' Theorem to calculate its length. Example : A steel rod is used to support a tree which is in danger of falling down. What is the height of the tree ? c 2 = a2 + b2 a = 17 - 8 2 2 2 a 2 = 225 c 17m rod b a a = 225 = 15m 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 8m Solving Real-Life Problems S4 www.mathsrevision.com 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. ( AC )2 = (DC )2 + ( AD )2 A B 13m b m C (DC )2 = 132 - 52 (DC )2 = 144 5m D Compiled by Mr. Lafferty Maths Dept. DC = 144 = 12m 13 Feb 2012 S4 Mixed Examples Now try Ex 3 Ch5 (page 58) www.m a th s re vis io n .c o m 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. ...
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## This note was uploaded on 02/13/2012 for the course MATH 115 115 taught by Professor Jones during the Spring '10 term at University of Phoenix.

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