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Form 5 Bearings 2B
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Chapter 3: Three Figure Bearings
Core (2A & 2B) Extension (2A)
• Interpret and use three-‐figure bearings measured clockwise from the north.
• Use scale drawings and trigonometrical ratios to solve problems involving bearings.
SEC Syllabus (2015): Mathemtics
Section 3.1 What are Bearings?
• There are many ways of giving bearings or directions. The most common method is the one in which NORTH is reckoned to be ZERO and angles are measured from the north in a CLOCKWISE direction.
• Usually 3 figures are given. o 055° is written for 55°. o 009° is written for 9°.
• In bearings when you draw angles you do not need to draw accurate angles with your protractor (if not otherwise stated).
For example, in this diagram the bearing of B from A is 060°.
A bearing can have any value from 0° to 360°. It is usual to give all bearings as three figures. This is known as a three-‐figure bearing. So, in the above example, the bearing is to be written as 060°, using three figures. Here are three more examples.
A
B
60°
N
N
Form 5 Bearings 2B
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There are eight bearings, which you should know. They are shown in the diagram.
D is on a bearing of 048° from C.
F is on a bearing of 110° from E.
H is on a bearing of 330° from G.
Form 5 Bearings 2B
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Example 1 : The bearing of A from B is 080°. What is the bearing of B from A?
Example 2: Draw sketches to illustrate the following situations.
a) C is on a bearing of 170° from H
b) B is on a bearing of 310° from W
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Example 3: A is due north from C. B is due east from A. B is on a bearing of 045° from C. Sketch the layout of the three points A, B and C.
Example 4 : Draw diagrams to solve the following problems.
a) The three-‐figure bearing of A from B is 070°. Work out the three-‐figure bearings of B from A.
b) The three-‐figure bearing of P from Q is 145°. Work out the three-‐figure bearings of Q from P.
c) The three-‐figure bearing of X from Y is 324°. Work out the three-‐figure bearings of Y from X.
Support Exercise Handout
Form 5 Bearings 2B
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Section 3.2 Bearings and Trigonometry
Example 1: Two fishing boats start sailing from the same place P. One of them sails 14km on a bearing of 060° to arrive at point A. The other boat sails for 12km on a bearing of 150° to arrive at point B.
a) Draw a sketch using this information b) Show that ∠APB = 90° c) Calculate the distance AB.
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Example 2: Two hikers depart from point P. John walks for 8km due North to point A while Patrick covers 11 km due East to point B. Find:
a) the direct distance AB
b) the bearing of A from B
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Example 4: From a point P, a man walks 9km north to Q, then 5km east to R. What is the bearing of R from P?
Support Exercise Handout
Form 5 Bearings 2B
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Section 3.3: Bearing and scale drawings
Step 1: Make a rough drawing of the object
Step 2: Mark all full size measurements on the diagram.
Step 3: Draw another sketch and put the scaled measurements on this one.
Step 4: Draw the accurate scale drawing.
Example 1: From one end, A, of a road the bearing of a building, L, is 015°. The other end of the road, B, is 300m due east of A. From B the bearing of the building is 320°. Using a scale of 1cm to 50m, make a scale diagram to find the distance of the building from A.
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Example 3: The diagram shows the positions of three British cities: London, Nottingham and Birmingham.
a) What is the bearing of: i. Nottingham from Birmingham ii. London from Birmingham iii. Birmingham from Nottingham
Nottingham
London
Birmingham
43°
48°
45 miles
100 miles
N
N
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b) Use 1cm to represent 10 miles, draw a scale diagram to show the positions of the three cities. Hence find the distance from London to Nottingham.
Support Exercise Handout