Bearings 20092021 I can measure and draw bearings

Bearings 20/09/2021 • I can measure and draw bearings

Intro Bearings 360/000 o N 1. Measured from North. 2. In a clockwise direction. 060 o 270 o 60 o W 090 o E 3. Written as 3 figures. S 180 o N W 145 o S N N E 145 o W 230 o S 315 o E W 315 o S E

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

N 360/000 o 030 o 330 o 045 o 315 o 290 o 075 o 090 o E W 270 o Control Tower Estimate the bearing of each aircraft from the centre of the radar screen. 110 o 250 o 135 o 225 o 170 o 200 o 180 o S Air Traffic Controller

N 360/000 o 7 325 o 010 o 8 310 o 040 o 1 ACE 060 o Controller contest 4 280 o 11 12 2 Estimate the bearing of each aircraft from the centre of the radar screen. 090 o E W 270 o 3 Control Tower 250 o 235 o 5 10 9 120 o 6 195 o 180 o S 155 o Air Traffic Controller

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

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

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

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

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

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

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. Thankyou 300 o 050 o Airfield (A) 283. 2 MHZ UHF Airfield (B) 306. 7 MHZ UHF

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 170 o 255 o Thankyou Airfield (B) 306. 7 MHZ UHF

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

• 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

Angles 20/09/2021 • I can calculate missing angles on a straight line

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

Angles on a straight line add to 180 o Oblique line 90 90 180 o Angles a + b = 180 o b b 70 o Angle b = 180 – 70 = 110 o a Horizontal line 35 o x Angle x = 180 – 35 = 145 o

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

• I can calculate missing angles on a straight line 10 ticks level 5 pack 3 page 17

Angles 20/09/2021 • I can calculate vertically opposite angles • I can calculate missing angles at a point

NON - PARALLEL LINES Vertically opposite angles are equal Try example

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

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

Angles at a Point d c b a Angles at a point add to 360 o Angle a + b + c + d = 3600

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

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

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

• I can calculate vertically opposite angles • I can calculate missing angles at a point 10 ticks level 5 pack 3 page 18 b

Angles 20/09/2021 • I can find missing angles in triangles

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

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

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

Calculating unknown Angles Example 1 Calculate angle a. 65 o a Angle a = 180 – (90 + 65) = 180 – 155 = 25 o Example 2 b Calculate angles a, b and c a c Since the triangle is equilateral, angles a, b and c are all 60 o (180/3)

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

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

• I can calculate missing angles in triangles 10 ticks level 5 pack 3 page 19 -20