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

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

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

Air Traffic Controller W 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

Air Traffic Controller W 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

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.

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.

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?

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.

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.

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

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

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

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

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

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

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.

Angles on a straight line add to 180o 90 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

Find the unknown angles x 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

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

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

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

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.

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

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

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 = 360 - (85 + 75 + 80) = 360 - 240 = 120o

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

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

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

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

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

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.

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

Calculate angles a, b and c Calculating unknown Angles Example 1 a 65o Calculate angle a. Angle a = 180 – (90 + 65) = 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)

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 –(65 + 65) = 180 – 130 = 50o Example 4 Calculate angles x and y y 130o x

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 – (15 + 27) = 180 – 42 = 138o

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