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Trigonometry Treasure Hunt

Develop critical thinking skills and apply trigonometry concepts to find missing angles and sides in a fun treasure hunt activity.

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Trigonometry Treasure Hunt

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  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 trigonometry 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: Ratio Variable Inverse 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 48 12 Write 0.6 as a fraction Write 912000 in standard form Write as a % Find 15% of $720 1) 2) 4) 3) 99 40 $108 = 3 6 6 5 -3 9.12 x 10 1.34 x 10 30% = = = = = 20 5 10 Write 0.00134 in standard form Value of: Expand and simplify: 8(x - 3) - 5(x - 6) Value of: 372 5) 6) 7) 8) 5 0 99x 48 x x 0.484848….. 100x 48.484848…… 2 = = = 4 = 8x - 24 – 5x + 30 1 = = = 32 = 3x + 6 EXTENSION . = . Factorise the following: Write 0.48 as a fraction x2 + 2x - 24 = ( )( ) x + 6 x - 4

  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 TRIGONOMETRY INTRODUCTION SomeOldHagCrackedAllHerTeeth OnAsparagus S O H C A H T O A o o A s H H A T C

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY EXAMPLES A 1) Work out the missing angles below: (a) H (b) (c) H A O O H A O SUBSTITUTE IN THE VALUES WRITE DOWN THE FORMULA LABEL THE SIDES SUBSTITUTE IN THE VALUES WRITE DOWN THE FORMULA LABEL THE SIDES SUBSTITUTE IN THE VALUES WRITE DOWN THE FORMULA LABEL THE SIDES 4 3 10 θ = θ = θ = 26.4°(3s.f) θ = 74.2°(3s.f) 59.0°(3s.f) θ = θ = 9 11 6 2) Work out the missing lengths below: (a) (c) H (b) H H O O A 10 4 4 3 b b sin θ = tan θ = cos θ = cos 33 = sin 64 = O A 6 11 9 14 9 A tan 46 WRITE DOWN THE FORMULA LABEL THE SIDES WRITE DOWN THE FORMULA LABEL THE SIDES SUBSTITUTE IN THE VALUES SUBSTITUTE IN THE VALUES WRITE DOWN THE FORMULA LABEL THE SIDES SUBSTITUTE IN THE VALUES -1 -1 -1 sin cos tan b = 9 x sin 64 b = b = 8.09cm(3s.f) 14 x cos 33 b = b = 11.7cm(3s.f) b =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  30. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY EXTENSION 1 (GRADE B) 1) 2) O x O 6cm θ 23° A 10cm A 100m Opposite Opposite x 6 tan θ = tan θ = tan θ = tan 23 = Adjacent Adjacent 10 100 6 θ = 10 x = 100 x tan 23 -1 tan θ = 31.0°(3s.f) 42.4m(3s.f) x =

  31. 100 tan 43 Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY EXTENSION 2 (GRADE B) 1) 2) x A 43° H 32m O x 100m 100m O 39° 1m Height above ground = Opposite Opposite x 100 tan θ = tan 43 = sin 39 = sin θ = 21.1m x Adjacent Hypotenuse 32 x = x = 32 x sin 39 x = 107m(3s.f) 20.1m(3s.f) x =

  32. 22.5 4.3 cos 42 cos 74 Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY EXTENSION 3 (GRADE B) 1) Find the side or angle marked x (b) (d) (a) (c) x 12cm 32° 15cm x x 42° 74° 74° 72° 20cm x 8.6cm 45cm x = 7.42cm H H H H A A A A 10 y 22.5 Adjacent Adjacent Adjacent Adjacent 4.3 cos 72 = cos θ = cos θ = cos θ = cos θ = cos θ = cos 74 = cos 42 = x x Hypotenuse Hypotenuse Hypotenuse Hypotenuse 15 12 -1 cos 10 x = x = y = θ = 12 x cos 72 15 3.71cm(3s.f) x = y = 48.2°(3s.f) 81.6cm(3s.f) x = 5.79cm(3s.f) θ =

  33. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY MINI-PLENARY – ASSESSING UNDERSTANDING H O A Work out the values of both x and y y Opposite Adjacent x cos θ = cos 36 = sin 36 = sin θ = 7 Hypotenuse Hypotenuse 7 y = x = 7 x sin 36 7 x cos 36 4.11(3s.f) y = x = 5.66(3s.f)

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

  35. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY PLENARY ACTIVITY– EXAM QUESTION (GRADE B) ABC and ACD are right-angled triangles. AD is parallel to BC. AB = 12cm, BC = 5cm and AD = 33.8cm. Calculate the size of angle ADC. D Pythagoras’ Theorem to calculate y y = 13cm y = √169 2 2 x 2 2 2 y = 25 + 144 y = 169 y = 5 + 12 13 x = 33.8 H 22.6°(3s.f) x = 33.8cm C O 13cm 13 Opposite sin x = sin x = y 33.8 Hypotenuse 5cm -1 sin B A 12cm

  36. 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 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.

  37. 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

  38. 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

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