1. The Sin e Ratio The Cos ine Ratio Mixed Problems The Tan gent Ratio

2. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

4. The Sine Ratio x° Sin x ° = Opposite Opp Hyp hypotenuse S4

5. 34° Sin x ° = Opp Opp Hyp 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 S O H C A H T O A Sine Ratio S4

6. x° Sin x ° = Opp Opp Hyp Hyp 6m 9m Sin x ° = 6 9 = 0.667 (3 d.p.) Sin x ° Find the x o S O H C A H T O A Sine Ratio S4

7. How do we find x °? 2 nd Sin ⁻ ¹ is written above To get this press Sin Followed by Sine Ratio =0.667 (3 d.p.) Sin x ° We need to use Sin ⁻ ¹ on the calculator. Sin Sin ⁻ ¹

8. x = Sin ⁻ ¹ 0.667 = 41.8 ° (1 d.p.) 2 nd Press Enter = 0.667 Sine Ratio = 0.667 (3 d.p.) Sin x ° Sin Sin ⁻ ¹

9. S O H C A H T O A 16 Feb 2010 Compiled by Mr. Lafferty Maths Dept. 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. 11.7m Sine Ratio 70 o h

10. S O H C A H T O A 16 Feb 2010 Compiled by Mr. Lafferty Maths Dept. Use the sine ratio to find the angle of the ramp. 20 m Sine Ratio x o 10m

11. S O H C A H T O A 72° Sin x ° = Opp Hyp Sin 72 ° = 5 r r = r = 5.3 km 5km A B C r A road AB is right angled at B. The road BC is 5 km. Calculate the length of the new road AC. Sine Ratio S4

12. Now try Ex 1 & 2 Ch 13 Page 148 Sine Ratio S4

13. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

15. Cos x ° = Adjacent Adj x° Hyp hypotenuse Cosine Ratio S4

16. S O H C A H T O A 40° Cos x ° = Opp Adj Hyp Hyp b 35mm Cos 40 ° = b 35 = b 35 x Cos 40 ° b = 35 x Cos 40 ° = 26.8mm (1 d.p.) Adj Find the adjacent length b Cosine Ratio S4

17. S O H C A H T O A x° Cos x ° = Opp Adj Hyp Hyp 45cm Cos x ° = 34 45 = 0.756 (3 d.p.) Cos x ° x = Cos ⁻ ¹0.756 =41 ° Adj 34cm S4 Find the angle x o Cosine Ratio

18. Now try Ex 3 Ch 13 Page 153 Cosine Ratio S4

19. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

21. 12 m How high is the tower? 60 ° Opp

22. 60 ° 12 m Adjacent Opposite hypotenuse Copy this!

23. Tan x ° = Opp Adj Tan 60 ° = Opp 12 = Opp 12 x Tan 60 ° Opp = 12 x Tan 60 ° = 20.8m (1 d.p.) Copy this!

24. So the tower’s 20.8 m high! Don’t worry, you’ll be trying plenty of examples!! 20.8m

25. Adj x° Tan x ° = Opposite Opp Adjacent S4 General

26. Example 65° Tan x ° = Opp Opp Adj Hyp h 8m Tan 65 ° = h 8 = h 8 x Tan 65 ° h = 8 x Tan 65 ° = 17.2m (1 d.p.) Adj S4 General Find the height h S O H C A H T O A

27. Extension Booklet

28. Past Paper Type Questions S O H C A H T O A Mixed Ratios S4

29. The Three Ratios www.mathsrevision.com Cosine Sine Tangent Sine Sine Tangent Cosine Cosine Sine www.mathsrevision.com opposite opposite opposite adjacent adjacent adjacent hypotenuse hypotenuse hypotenuse S4

30. C A H T O A S O H Mixed Ratios S4 Sin x ° = O pp H yp Cos x ° = A dj H yp Tan x ° = O pp A dj

31. S O H C A H T O A 1. Write down Process Identify what you want to find what you know 3. 2. Mixed Ratios S4 Copy this!

32. Past Paper Type Questions (4 marks) S O H C A H T O A Mixed Ratios S4

33. Past Paper Type Questions S O H C A H T O A Mixed Ratios S4

34. Past Paper Type Questions S O H C A H T O A 4 marks Mixed Ratios S4

35. Past Paper Type Questions S4 S O H C A H T O A Mixed Ratios

36. Past Paper Type Questions S4 (4marks) S O H C A H T O A Mixed Ratios

37. Past Paper Type Questions S4 S O H C A H T O A Mixed Ratios

38. Past Paper Type Questions S4 (4marks) S O H C A H T O A Mixed Ratios

39. Now try Ex 4 Ch 13 Page 157 Mixed Ratios S4