2. Trigonometry means “triangle” and “measurement”. Adjacent Opposite x°x°x°x° hypotenuse We will be using right-angled triangles. The Tan Ratio Trigonometry

3. 60° 12 m Adjacent Opposite hypotenuse Copy this! The Tan Ratio Finding the ‘Opposite’ side

4. Tan x° = Opp Adj Tan 60° = Opp 12 = Opp12 x Tan 60° Opp =12 x Tan 60°= 20.8m (1 d.p.) Copy this! The Tan Ratio Finding the ‘Opposite’ side O TanA

5. 47° 20 m Adjacent Opposite hypotenuse Copy this! The Tan Ratio Finding the ‘Opposite’ side

6. Tan x° = Opp Adj Tan 47° = Opp 20 = Opp20 x Tan 47° Opp =20 x Tan 47°= 21.4m (1 d.p.) Copy this! The Tan Ratio Finding the ‘Opposite’ side O TanA

7. Use the tan ratio to find the height h of the tree to 1 decimal place. 47 o 8m rod The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 47° = h 8 8 x Tan 47°= h 8 x Tan 47°= 8.6m (1 d.p.) h O TanA

8. Use the tan ratio to calculate how far the ladder is away from the building. 45 o 12m ladder d m The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 45° = 12 d d x tan 45º = 12 d = 12 tan 45º = 12m O TanA

9. 6o6o Aeroplane 1.58 km Lennoxtown Airport Q1.An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present. It is at a height of 1.58 km above the ground. It ‘s angle of descent is 6 o. How far is it from the airport to Lennoxtown? Example 2 The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 6° = 1.58 a a = 1.58 tan 6º = 15.03km (2 d.p) ? O TanA

10. Using Tan to calculate angles

11. 18 12 Example x°x° Tan x° = Opp Adj Hyp 12m Tan x° = Adj 18m Calculate the tan x o ratio Q P R The TAN Ratio Calculating the angle

12. The TAN Ratio Calculating the angle How do we find x°? We need to use Tan ⁻ ¹ on the calculator. 2 nd Tan ⁻ ¹is written above Tan Tan ⁻ ¹ To get this press Tan Followed by Calculate the size of angle x o 18 12 Tan x° =

13. x = Tan ⁻ ¹ = 56.3° (1 d.p.) 2 nd Tan Tan ⁻ ¹ Press Enter = The TAN Ratio Calculating the angle 18 12 Tan x° = 18 12 18 12

14. Process 1.Identify Hyp, Opp and Adj 2.Write down ratio Tan x o = Opp Adj 3.Calculate x o 2 nd Tan Tan ⁻ ¹ The TAN Ratio Calculating the angle

15. Use the tan ratio to calculate the angle that the support wire makes with the ground. xoxo 11m 4 m The TAN Ratio Calculating the angle hyp opp adj Tan x° = Opp Adj 11 4 Tan x° =

16. 11 Tan x° = 4 The TAN Ratio Calculating the angle 2 nd Tan Tan ⁻ ¹ Press Enter = 11 4 x = Tan ⁻ ¹ 11 = 70.02° (2 d.p.) 4

17. The Sine Ratio x°x°x°x° Sin x° = O p p o s i t e Opp Hyp h y p o t e n u s e Trigonometry

18. Example 34° Sin x° = Opp Hyp h 11cm Sin 34° = h 11 = h 11 x Sin 34° h =11 x Sin 34°= 6.2cm (1 d.p.) Find the height h The Sine Ratio Trigonometry O SinH Adj

19. The support rope is 11.7m long. The angle between the rope and ground is 70 o. Use the sine ratio to calculate the height of the flag pole. 70 o h 11.7m The Sine Ratio Trigonometry hyp opp adj Sin x° = Opp Hyp Sin 70° = h 11.7 O SinH = h11.7 x Sin 70° h =11.7 x Sin 70°= 11.0cm (1 d.p.)

20. Example 72° Sin x° = Opp Hyp Sin 72° = 5 r r = 5.3 km 5km AB C r A road AB is right angled at B. The road BC is 5 km. Calculate the length of the new road AC. The Sine Ratio Trigonometry Hyp Opp Adj O SinH 5 Sin 72º

21. Using Sin to calculate angles

22. Using Sine ratio to find an angle Example x°x°x°x° Sin x° = Opp Hyp 6m 9m Sin x° = 6 9 Find the x o Trigonometry Adj

23. =Sin x° How do we find x°? We need to use Sin ⁻ ¹ on the calculator. 2 nd Sin ⁻ ¹is written above Sin Sin ⁻ ¹ To get this press Sin Followed by Using Sine ratio to find an angle Trigonometry 6 9

24. x = Sin ⁻ ¹ = 41.8° (1 d.p.) =Sin x° 2 nd Sin Sin ⁻ ¹ Press Enter = 6 9 Using Sine ratio to find an angle Trigonometry 6 9 6 9 () ()

25. Use the sine ratio to find the angle of the ramp. xoxo 10m 20 m Using Sine ratio to find an angle Trigonometry

26. The Cosine Ratio Cos x° = Adjacent Adj x°x°x°x° Hyp h y p o t e n u s e Trigonometry opposite

27. Example 40° Cos x° = Opp Adj Hyp b 35mm Cos 40° = b 35 = b35 x Cos 40° b =35 x Cos 40°= 26.8mm (1 d.p.) Adj Find the length b The Cosine Ratio Trigonometry A CosH

28. Example 33° Cos x° = Opp Adj Hyp 26 c Cos 33° = 26 c = b c= 31.0mm (1 d.p.) Adj Find the length c The Cosine Ratio Trigonometry A CosH c = 26 cos 33

29. Using Cos to calculate angles

30. The Cosine Ratio Example x°x°x°x° Cos x° = Opp Adj Hyp 45cm Cos x° = 34 45 = 0.756 (3 d.p.)Cos x° x = Cos ⁻ ¹0.756 =41° Adj 34cm Trigonometry Find the angle x o

31. Sin x° = Opp Hyp Cos x° = Adj Hyp Tan x° = Opp Adj C A HT O AS O H Trigonometry Mixed Problems

32. S O H C A H T O A Copy this! 1. Write down Process Identify what you want to find what you know 3. 2. Trigonometry Mixed Problems

33. Past Paper Type Questions (4 marks) S O H C A H T O A Trigonometry Mixed Problems

34. Past Paper Type Questions S O H C A H T O A Trigonometry

35. Past Paper Type Questions S O H C A H T O A 4 marks Trigonometry

36. Past Paper Type Questions S O H C A H T O A Trigonometry

37. Past Paper Type Questions General (4marks) S O H C A H T O A Trigonometry