1. Bearings I can measure and draw bearings Learning objectives
29/04/2019
I can measure and draw bearings

2. Intro Bearings 1. Measured from North. 2. In a clockwise direction.
3. Written as 3 figures. N S E W
315o
145o
315o
230o
230o
145o

3. A 360o protractor is used to measure bearings.
Use your protractor to measure the bearing of each point from the centre of the circle (Worksheet 1) N S E W
090o
360/000o
270o
180o
350o
020o NW
315o NE
045o
290o
080o
250o SW
225o
210o
110o
160o SE
135o
360 degree protractor

4. Air Traffic ControllerW E N S
Air Traffic Controller
Control Tower
030o
330o
Estimate the bearing of each aircraft from the centre of the radar screen.
315o
045o
290o
075o
250o
225o
200o
170o
135o
110o

5. Air Traffic ControllerW E N S
Air Traffic Controller
Control Tower
010o 1 2 12 10 9 8 4 11 7 6 5 3
325o
Estimate the bearing of each aircraft from the centre of the radar screen.
ACE
Controller
contest
040o
310o
060o
280o
250o
235o
195o
120o
155o

6. B from A Bearings B A Measuring the bearing of one point from another.
To Find the bearing of B from A. B A
060o N
B from A
1. Draw a straight line between both points.
2. Draw a North line at A.
3. Measure the angle between.

7. Bearings B A Measuring the bearing of one point from another.
To Find the bearing of A from B. B A N
1. Draw a straight line between both points.
240o
2. Draw a North line at B.
3. Measure angle between.

8. How are the bearings of A and B from each other related and why?
Measuring the bearing of one point from another. N
060o B A
240o
How are the bearings of A and B from each other related and why?

9. Bearings P Q Measuring the bearing of one point from another.
To Find the bearing of Q from P. N
118o
1. Draw a straight line between both points.
2. Draw a North line at P.
3. Measure angle between.

10. Bearings P Q Measuring the bearing of one point from another.
To Find the bearing of P from Q. N
298o
1. Draw a straight line between both points.
2. Draw a North line at Q.
3. Measure angle between.

11. How are the bearings of P and Q from each other related and why?
Measuring the bearing of one point from another. N P Q
118o
298o
How are the bearings of P and Q from each other related and why?
Worksheet 3

12. Bearings: Fixing Position
Trainee pilots have to to learn to cope when the unexpected happens. If their navigation equipment fails they can quickly find their position by calling controllers at two different airfields for a bearing. The two bearings will tell the pilot where he is. The initial call on the controllers radio frequency will trigger a line on the radar screen showing the bearing of the calling aircraft.
Airfield (A)
283.2 MHZ UHF
Airfield (B)
306.7 MHZ UHF
050o
300o
Thankyou

13. Bearings: Fixing Position
Trainee pilots have to to learn to be cope when the unexpected happens. If their navigation equipment fails they can quickly find their position by calling controllers at two different airfields for a bearing. The two bearings will tell the pilot where he is. The initial call on the controllers radio frequency will trigger a line on the radar screen showing the bearing of the calling aircraft.
Airfield (A)
283.2 MHZ UHF
Airfield (B)
306.7 MHZ UHF
170o
255o
Thankyou

14. A B
1. Find the position of a point C, if it is on a bearing of 045o from A and 290o from B.
2. Find the position of a point D if it is on a bearing of 120o from A and 215o from B. C D

15. Success Criteria I can measure and draw bearings
10 ticks level 6 pack 2 page 29 or 30
10 Ticks level 6 pack 2 page 33-36

16. Angles I can calculate missing angles on a straight line
Learning objectives
29/04/2019
I can calculate missing angles on a straight line

17. This angle is also a right angle.
Angles on a Line
When a vertical line and a horizontal line meet the angle between them is 90o, a right angle.
90o, a right angle
Vertical line
This angle is also a right angle. 90
Horizontal line
This explains why the angles on a straight line add to 180o.
The lines are said to be perpendicular to each other.

18. Angles on a straight line add to 180o90
Angles on a straight line add to 180o
180o
Oblique line
Horizontal line a b
Angles a + b = 180o
70o b x
35o
Angle b = 180 – 70 = 110o
Angle x = 180 – 35 = 145o

19. Find the unknown anglesx
47o
Find the unknown angles 1
114o y 2 3 4
76o a
82o b
Angle x = 180 – 47 = 133o
Angle y = 180 – 114 = 66o
Angle a = 180 – 76 = 104o
Angle b = 180 – 82 = 98o

20. Success Criteria I can calculate missing angles on a straight line
10 ticks level 5 pack 3 page 17

21. Angles I can calculate vertically opposite angles
Learning objectives
29/04/2019
I can calculate vertically opposite angles
I can calculate missing angles at a point

22. Vertically opposite angles are equal
NON - PARALLEL LINES
Try example
Vertically opposite angles are equal

23. This diagram helps explains why angles at a point add to 360o.90
Vertical
Horizontal
Remember: Angles at a on a line add to 180o 90 90
This diagram helps explains why angles at a point add to 360o.

24. This explains why angles at a point add to 360o.90
Vertical
Horizontal 1 2
360o
360o
360o 3 4
This explains why angles at a point add to 360o.
360o
360o

25. Angles at a point add to 360ob c d
Angles at a point add to 360o
Angle a + b + c + d = 3600

26. Angles at a Point Example 1: Find angle a. a 75o 85o 360o 80o +90
360o
75o
85o
80o a
Example 1: Find angle a. 85 75 80 +
240
Angle a = ( )
= = 120o

27. Angles at a Point Example 2: Find angle x. 105o x 360o 100o +90
360o 90
100
105 +
295
Angle x = ( )
= = 65o

28. 1
360o in a circle.
What does it mean?
90o
360o 4 2
270o 3
180o

29. Success Criteria I can calculate vertically opposite angles
I can calculate missing angles at a point
10 ticks level 5 pack 3 page 18b

30. Angles I can find missing angles in triangles Learning objectives
29/04/2019
I can find missing angles in triangles

31. Angles In Triangles Types of Triangles Isosceles triangle
2 equal sides
2 equal angles (base)
Equilateral Triangle
3 equal sides
3 equal angles.
Scalene triangle
3 unequal sides
3 unequal angles

32. Any triangle containing a 90o angle is a right-angled triangle
An isosceles or a scalene triangle may contain a right angle.
Right-angled
isosceles triangles.
Right-angled
scalene triangle.

33. The angle sum of a triangle = 1800
To determine the angle sum of any Triangle
How can we use this to help us?
Take 3 identical copies of this triangle like so: 3 1 2
Angles on a straight line add to 180o
These are the same angles as in the triangle!
The angle sum of a triangle = 1800

34. Calculate angles a, b and c
Calculating unknown Angles
Example 1 a
65o
Calculate angle a.
Angle a = 180 – ( )
= 180 – 155 = 25o
Example 2
Calculate angles a, b and c a b c
Since the triangle is equilateral,
angles a, b and c are all 60o (180/3)

35. Calculating unknown Angles
Example 3 a
65o
Calculate angle a. b
Angle a = 65o (base angles of an isosceles triangle are equal).
Angle b = 180 –( )
= 180 – 130 = 50o
Example 4
Calculate angles x and y y
130o x

36. Calculate angles a and b.
Calculating unknown Angles
Example 5
Calculate angles a and b. b a
Example 6
Calculate angle a
15o
27o a
Angle a = 180 – ( )
= 180 – 42 = 138o

37. Success Criteria I can calculate missing angles in triangles
10 ticks level 5 pack 3 page 19-20