Which ones are you using?

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

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

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK 74 12 Write 0.9 as a fraction Write 690000 in standard form Write as a % Find 15% of $680 1) 2) 4) 3) 99 20 $102 = 9 5 -4 60% 2.6 x 10 6.9 x 10 = = = 10 Write 0.00026 in standard form Value of: Expand and simplify: 5(x - 2) - 2(x - 5) Value of: 186 5) 6) 7) 8) 3 0 99x 74 x 100x 74.747474…… x 0.747474….. 2 = = = 25 = 5x - 10 – 2x + 10 1 = = = 125 = 3x EXTENSION . = . Factorise the following: Write 0.74 as a fraction x2 + 2x - 35 = ( )( ) x + 7 x - 5

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY 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 3s.f. where appropriate. (d) sin 0 5 4 (c) sin 90 (b) sin 26 (a) sin 54 8 7 0 0.809 0.438 1 = = = = (h) cos 0 (g) cos 90 (f) cos 26 (e) cos 54 1 0.588 0.899 0 = = = = (l) tan 0 (k) tan 89 (j) tan 26 (i) tan 54 0 1.38 0.488 57.3 = = = = (n) 6 cos 24 (o) 8 tan 44 (m) 4 sin 62 3.53 5.48 7.73 = = = (r) (p) (q) 5.26 = (s) tan (t) cos 8 9 5 -1 -1 sin 72 tan 18 cos 35 SHIFT tan SHIFT cos 51.3 9.77 27.7 29.7 = = = =

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

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY 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 A O A H A O O A A (f) (h) (e) (g) A O A H O H H O H

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TANGENT FUNCTION EXAMPLES (b) (a) O H O H b 8cm 64° θ A 6cm A 11cm Find the length of side b Find the angle θ SUBSTITUTE IN THE VALUES SUBSTITUTE IN THE VALUES LABEL THE SIDES LABEL THE SIDES WRITE DOWN THE FORMULA WRITE DOWN THE FORMULA Opposite Opposite 8 b tan θ = tan θ = tan θ = tan 64 = Adjacent Adjacent 11 6 -1 tan 8 θ = b = 6 x tan 64 11 b = 12.3cm(3s.f) θ = 36.0°(3s.f)

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TANGENT FUNCTION TASK (GRADE B) (a) (b) (c) (d) A O O A A A O O Work out θ Work out θ Work out θ Work out θ (e) (f) (g) (h) O A O A A A O O Find the value of x Find the value of x Find the value of x Find the value of x

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TANGENT FUNCTION EXTENSION (GRADE B) 1) Angle θ has a tangent of . Calculate the missing lengths in these triangles. (a) (b) (c) (d) A O O O A A O A x2 x10 8 40 x4 16 x8 32 x = 8 x = 40 x = 20 10 50 x2 20 x10 x4 x8 40 2) Find the values of θ below: 5.27m x = 40 (a) (b) (c) (d) A O A 3m 6m O A A O 16m O

10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TANGENT FUNCTION MINI-PLENARY – SPOT THE MISTAKE 2) 1) Find the length of x Find the angle θ O A H O

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

12. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TANGENT FUNCTION PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B) A window cleaner leans his ladder against a wall so that the foot of the ladder is 10m from the wall. The vertical length from the ground to where the ladder rests against the wall is 8m. What angle does the ladder make with the ground? θ 8m 8 θ = 10 θ = 38.7°(3s.f) Opposite 8 tan θ = tan θ = 10 Adjacent 10m -1 tan

13. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about using the tangent function 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.

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

15. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? 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