GCSE Bearings Dr J Frost jfrosttiffin kingston sch
GCSE : : Bearings Dr J Frost (jfrost@tiffin. kingston. sch. uk) Objectives: (a) Measure bearings using a protractor. (b) Construct bearings, involving map scales (c) Solve bearings problems using given angles. Last modified: 28 th January 2018
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Q Starter Puzzle Here some aerial pictures of various airport runways Dr Frost has been on. Can you work out what the numbers mean? Heathrow - London JFK – New York Beijing Capital International Airport Solution: If we add a 0 on the end, we get the angle clockwise from North the runway faces! Portland International Airport - Oregon Hilo Airport - Hawaii Euro. Airport – Basel. Mulhouse-Freiberg Rhodes Airport Greece
Bearings We understand an ‘angle’ to mean ‘the amount of turn’. Bearings are more specifically the amount of turn clockwise, starting from North. ! A bearing is an angle measured clockwise from North. We use 3 digits. B Q A ? Bearings can be thought of as a numerical version of cardinal directions (North, West, etc) C Q Q Q E Historical reason for 3 digits? Bearings used to be transmitted digit by digit from ship to ship. Were some bearings two digits, it would be ambiguous whether two digits was intended or a digit was lost in transmission. The bearing of: B from A A from B C from A Q D D from A A from D A from E E from A 000 ? 180 ? 090 ? 225 ? 045 ? 135 ? 315 ?
Measuring Bearings Fro Tip: You’re measure the angle at whatever appears just after the word ‘from’. N N Click to Fromeasure > What do you notice about the two bearings? ?
Test Your Understanding Question on provided sheet. B from A A from B C from B D from C A from D D from A 116 ? 296 ? 073 ? 228 ? 334 ? 154 ?
Exercise 1 – Measuring Bearings (On supplied sheet) 1 In each diagram determine: (without a protractor) (i) the bearing of B from A and (ii) the bearing of A from B. a ? b ? c ? d ? e e d 2 c b ? ? Continued on next slide…
Exercise 1 – Measuring Bearings 3 (On supplied sheet) 7 N ? Cambridge N ? ? London 8 4 N Munich ? ? N Hamburg 5 ? N Argos Lidl 6 ? ? N N A N N B C ? ? ?
You have a map of Kingston-upon-Thames… Scale 1: 300 What does this scale mean? Real life distances are 300 times larger than map distances. ? e. g. 1 cm on the map represents 300 cm in real life. 75 cm Tiffin John Lewis What distance is this in real life? ?
Further Examples A map scale is 1 : 20 000. A distance is measured on a map of 4 cm. What does this represent in real life? ? 5 cm : 2 km 5 cm : 2000 m 5 cm : 200 000 cm 1 : 40 000 When scaling, be consistent with the unit used. Write the ratio of the two distances (with units), and convert one distance so that the units are the same. ?
Test Your Understanding [Edexcel IGCSE Nov-2010 -4 H Q 8] The scale of a map is 1 : 50 000 On the map, the distance between two schools is 19. 6 cm. Work out the real distance between the schools. Give your answer in kilometres. ? [Edexcel GCSE(9 -1) Mock Set 2 Spring 2017 2 F Q 10] A map has a scale of 1 cm to 25 km. The distance between the cities of Edinburgh and Bristol is 500 km. What is the distance on the map between these two cities? ?
Constructing Maps You can combine your knowledge of map scales with that of bearings in order to plot locations on a map. N Alice Bob! Use your pencil to mark the correct angle. Click to start Fromanimation >
Further Example You can combine your knowledge of map scales with that of bearings in order to plot locations on a map. N Tarquin Chelsea Click to start Fromanimation >
Exercise 2 – Constructing Bearings (On supplied sheet) 3 1 ? ? 5 cm N N 4. 1 cm 2 4 N ? N 6. 2 cm N 6 km ? 4 km Distance: 7. 8 km
Exercise 2 – Constructing Bearings 5 (On supplied sheet) 7 ? N ? 3 m Distance: 4. 3 m ? 7 m 8 6 ? 9 6. 5 m 5 m ? N ?
Bearings calculations using known angles Often in questions, angles will already be given to you. You need to use your knowledge of angle laws to calculate bearings. Recap: Alternate angles ? are equal. Corresponding ? equal. angles are ? ?
Examples Always start by drawing the bearing in. Recall that we go clockwise from North and we draw the angle at the point after the word ‘from’.
Harder Example Note that when we draw the diagram, we need not draw the angles accurately, because we are using angle laws, and not a protractor, to determine the answer. Put angles given in question on diagram.
Test Your Understanding 1 ? 2 ? ?
Exercise 3 – Bearings using angle laws 2 1 (On supplied sheet) 4 ? ? ? 5 3 ? ? ?
Exercise 3 – Bearings using angle laws 6 [Edexcel IGCSE Jan 2014(R)-4 H Q 10 b] The diagram shows the positions of a yacht Y, a ship S and a beacon B. The bearing of B from Y is 228°. The bearing of S from Y is 118°. (a) Find the size of the angle BYS. (b) Given also that BY = SY, find the bearing of S from B. ? ? 7 (On supplied sheet) [Edexcel IGCSE Nov 2009 -4 H Q 3 b] The bearing of B from A is 062°. C is due south of B. AB = CB. Work out the bearing of C from A. ?
Exercise 3 – Bearings using angle laws 9 8 ? ? (On supplied sheet)
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