Creative Thinker Effective Participator Independent Enquirer Reflective Learner

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills LESSON OBJECTIVES Self Manager Team Worker Which ones are you using? Always aim high! We are learning to: - Finding connections between different words. (Which PLT skills? ) - Accurately use trigonometry to calculate missing sides and angles in right angled triangles. (Grade B) Where are we in our journey? AUTHOR www. mistrymaths. co. uk Real life cross/curricular links?

Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner BRAIN IN GEAR Self Manager Team Worker Which ones are you using? EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: OATIR Ratio AVRELIAB Variable SENIVER Inverse EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner STARTER Self Manager Team Worker Which ones are you using? TASK 12 40 1)Write = 0. 6 as 2) Write 912000 in 3) Write a fraction standard form as a % 5 6 6 3 = = = 9. 12 x 10 = 30% 20 10 5 4) Find = 15% of $720 $108 5)Write 0. 00134 in 6) Expand simplify: 7) Value of: 8) Value of: 5 0 2 standard form 8(x - 3) - 5(x - 6) 372 4 -3 = 1. 34 x 10 = 8 x - 24 – 5 x + 30 = 1 = 32 = 3 x + 6 EXTENSION . . Write 0. 48 as a fraction x = 0. 484848…. . 100 x = 48. 484848…… 99 x = 48 48 x= 99 Factorise the following: x 2 + 2 x - 24 = ( x + 6 )( x - 4 )

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? Make sure your calculator is set to D or Deg not R or Rad INTRODUCTION – USING YOUR CALCULATOR Find the values, rounding the answers to 3 s. f. where appropriate. (a) sin 54 (b) sin 26 (c) sin 90 (d) sin 0 = 0. 809 = 0. 438 = 1 (e) cos 54 (f) cos 26 (g) cos 90 (h) cos 0 = 1 = 0. 588 = 0. 899 = 0 (i) tan 54 (j) tan 26 (k) tan 89 (l) tan 0 = 1. 38 = 0. 488 = 57. 3 5 (p) (n) 6 cos 24 (o) 8 tan 44 (m) 4 sin 62 sin 72 = 3. 53 = 5. 48 = 7. 73 = 5. 26 5 4 (q) 8 (r) 9 (s) tan-1 7 (t) cos-1 8 cos 35 = 9. 77 tan 18 = 27. 7 SHIFT tan = 29. 7 SHIFT cos = 51. 3

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? INTRODUCTION – LABELLING SIDES CORRECTLY This is opposite the right-angle. This is opposite the angle. This is next to the angle.

Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner TRIGONOMETRY Self Manager Team Worker Which ones are you using? INTRODUCTION – LABELLING SIDES CORRECTLY Label the sides of the triangles below with opposite, adjacent and hypotenuse: (b) (d) (a) (c) A H O H H O O A A A (e) O (f) A H A O H O A (g) H (h) A H O O H

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Which ones are you using? PLT Skills TRIGONOMETRY INTRODUCTION Some Old Hag Cracked All Her Teeth On Asparagus SOH CAH TOA o s H Team Worker A o C H T A

Creative Thinker Effective Participator PLT Skills EXAMPLES Independent Enquirer Reflective Learner TRIGONOMETRY Self Manager Which ones are you using? A 1) Work out the missing angles below: (a) H O H (b) A Team Worker A (c) O H O SUBSTITUTE WRITELABEL DOWNIN THE THE THE SIDES FORMULA VALUES SUBSTITUTE WRITELABEL DOWNIN THE THE SIDES FORMULA VALUES 4 3 10 sin θ = cos θ = tan θ = 9 11 6 3 10 -1 4 θ = 74. 2°(3 s. f) θ = tan -1 θ = 59. 0°(3 s. f) θ = sin 9 θ = 26. 4°(3 s. f) θ = cos-1 11 6 2) Work out the missing lengths below: (a) (b) H H O (c) O H A A WRITE DOWNTHE FORMULA LABEL SIDES SUBSTITUTE IN THE VALUES b sin 64 = 9 O A WRITE DOWNTHE FORMULA LABEL SIDES SUBSTITUTE IN THE VALUES SUBSTITUTE WRITE DOWNTHE FORMULA LABEL SIDES IN THE VALUES b cos 33 = 14 4 b = 9 x sin 64 b = 8. 09 cm(3 s. f) b = 14 x cos 33 b = 11. 7 cm(3 s. f) b = b= tan 46

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? TASK 1 (GRADE B) – FINDING MISSING ANGLES (a) (b) H O (c) H O (d) A A A Work out θ (e) H (f) A (h) O Work out θ 2 m (g) H O Work out θ A O H 18 m Work out θ

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? TASK 2 (GRADE B) – FINDING MISSING SIDES (a) O (b) A Find the value of x (e) H A Find the value of x H O Find the value of x (f) (c) A Find the value of x (g) A O Find the value of x (d) H A H Find the value of x H O Find the value of x (h) A O Find the value of x

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 3 (GRADE B) – TREASURE HUNT Self Manager Team Worker Which ones are you using?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 4 (GRADE B) – TREASURE HUNT Self Manager Team Worker Which ones are you using?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Draw a 3 x 3 grid as shown below: Self Manager Team Worker Which ones are you using? Place any nine numbers below into the grid (repeats forbidden) Cos 20 10 Tan-1 Hyp Sin Adj 17 Sin-1 7/25 23/35 Cos-1 13/25 Opp Tan 23/20

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? Name the trigonometry ratio used to work out: ? 10 cm 32 o Team Worker Sin

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Team Worker Which ones are you using? What is the name of side with the ? ? 32 o Hyp

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? Name the trigonometry ratio used to work out: Tan 10 cm 32 o ? Team Worker

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? Opposite = ? x sin 25 10 cm Opposite 25 o 7 cm Team Worker 10

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Team Worker Which ones are you using? What is the name of side with the ? 32 o ? Adj

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? Name the trigonometry ratio used to work out: ? 10 cm 15 cm Team Worker Cos

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? x = cos ? -1 X 25 cm 13 cm 7 cm Team Worker 13 25

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? Name the trigonometry ratio used to work out: x= ? 23 cm 10 cm x Team Worker 10 23 Sin -1

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? 13 cm 7 cm x = sin ? -1 X 25 cm Team Worker 7 25

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Team Worker Which ones are you using? What is the name of side with the ? ? 32 o Opp

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? x = tan -1 20 cm X 17 cm 10 cm Team Worker ? 10 17

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? Name the trigonometry ratio used to work out: x= ? 12 cm 10 12 x Tan -1 10 cm Team Worker

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? 32 o Opposite = ? x sin 32 20 cm Team Worker 20

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is ? : x= ? 20 32 32 cm x 20 cm Team Worker Cos -1

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? x = tan ? -1 35 cm X 20 cm 23 cm Team Worker 23 20

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY TASK 5 (GRADE B) – BINGO Self Manager Which ones are you using? What is value of ? x = sin ? -1 35 cm X 20 cm Team Worker 23 cm 23 35

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY EXTENSION 1 (GRADE B) 1) 2) O 6 cm O Self Manager Team Worker Which ones are you using? x θ 23° 10 cm A Opposite Adjacent tan θ = 6 10 -1 6 θ = tan 10 tan θ = 31. 0°(3 s. f) 100 m A Opposite Adjacent x tan 23 = 100 tan θ = x = 100 x tan 23 x = 42. 4 m(3 s. f)

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY EXTENSION 2 (GRADE B) 1) 2) Self Manager Team Worker Which ones are you using? x. A 43° H 32 m x 39° O O 100 m 1 m Opposite Hypotenuse x sin 39 = 32 sin θ = x = 32 x sin 39 x = 20. 1 m(3 s. f) Height above ground = 21. 1 m Opposite Adjacent tan 43 = 100 x= tan 43 tan θ = x = 107 m(3 s. f)

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills TRIGONOMETRY EXTENSION 3 (GRADE B) 1)Find the side or angle marked x (a) x (b) (c) 15 cm 12 cm x 42° 8. 6 cm 20 cm A Adjacent cos θ = Hypotenuse 4. 3 cos 42 = x 4. 3 x= cos 42 x = 5. 79 cm(3 s. f) (d) x 32° 74° x x = 7. 42 cm H A Team Worker Which ones are you using? 72° H H Self Manager 74° 45 cm H A A Adjacent cos θ = Hypotenuse 22. 5 y 10 cos 74 = cos 72 = cos θ = x 12 15 10 22. 5 -1 x= y = 12 x cos 72 θ = cos 15 cos 74 θ = 48. 2°(3 s. f) y = 3. 71 cm(3 s. f) x = 81. 6 cm(3 s. f)

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? MINI-PLENARY – ASSESSING UNDERSTANDING H O A Work out the values of both x and y Adjacent Hypotenuse x cos 36 = 7 cos θ = x = 7 x cos 36 x = 5. 66(3 s. f) Opposite Hypotenuse y sin 36 = 7 sin θ = y = 7 x sin 36 y = 4. 11(3 s. f)

Creative Thinker Effective Participator PLT Skills Independent Enquirer DISCOVERY Reflective Learner Self Manager Team Worker Which ones are you using? LINK BACK TO OBJECTIVES - Accurately use trigonometry to calculate missing sides and angles in right angled triangles. What grade are we working at?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you PLT Skills TRIGONOMETRY using? PLENARY ACTIVITY– EXAM QUESTION (GRADE B) ABC and ACD are right-angled triangles. AD is parallel to BC. AB = 12 cm, BC = 5 cm and AD = 33. 8 cm. Calculate the size of angle ADC. Opposite sin x = Pythagoras’ Theorem D Hypotenuse to calculate y 2 x H 33. 8 cm O 13 cm y A 12 cm C 5 cm B 2 2 y = 5 + 12 y 2 = 25 + 144 y 2 = 169 y = √ 169 y = 13 cm sin x = 13 33. 8 -1 13 x = sin 33. 8 x = 22. 6°(3 s. f)

What have you learnt? Draw your brain In your brain, write or draw everything you can remember about using the trigonometry to calculate missing sides and angles in right angled triangles. It can be a skill or a reflection, or something else that might be prominent in your brain. Where are we in our journey? What grade are we working at?

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Which ones are you Enterprise Skills. SELF ASSESSMENT Plenary using? Activity How well do you understand the task? . I don’t understand I nearly understand www. mistrymaths. co. uk I fully understand

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. SELF ASSESSMENT Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www. mistrymaths. co. uk Responsible Citizen Team Worker Which ones are you using?