Defining the Tangent ratio in Trigonometry. Small changes between slides so can be clicked through quickly.

1. Defining the sine, Tangent and tangent ratios for angles in right-angled trianglesPart 3 - Tangent

2. The Tangent Ratio

3. The Tangent Ratio

4. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent

5. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

6. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

7. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

8. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

9. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

10. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 Remember:

11. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 Remember:

12. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 T Remember:

13. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 T Remember:

14. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 TO Remember:

15. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 TO Remember:

16. The Tangent Ratio The Tangent of an angle is defined as the ratio between the Opposite and the Adjacent 𝑻𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 TOA Remember:

17. The Tangent Ratio Remember: TOA Tangent of 𝜃 is equal to 𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓

18. The Tangent Ratio Remember: TOA Tangent of 𝜃 is equal to 𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓

19. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to 𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓

20. The Tangent Ratio Remember: TOA Tangentof 𝜃is equal to 𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓

21. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to 𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓

22. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝒐𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Opposite

23. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Opposite

24. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝒂𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

25. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

26. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

27. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

28. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

29. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

30. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

31. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

32. The Tangent Ratio Remember: TOA Tangentof 𝜃 is equal to𝑶𝒑𝒑𝑨𝒅𝒋=𝒔𝒕=𝟕.𝟐𝟏𝟏𝟎.𝟓 Adjacent Opposite

33. The Tangent Ratio 𝐓angent𝜃=OppositeAdjacent

34. The Tangent Ratio 𝐓angent𝜃=OppositeAdjacent

35. The Tangent Ratio Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent

36. The Tangent Ratio Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent

37. The Tangent Ratio Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent

38. The Tangent Ratio Tangent=𝒔𝑨 𝐓angent𝜃=OppositeAdjacent

39. The Tangent Ratio Tangent=𝒔𝑨 𝐓angent𝜃=OppositeAdjacent

40. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent

41. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent

42. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent

43. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨

44. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨

45. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨

46. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝑨

47. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝑨

48. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

49. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

50. The Tangent Ratio Tangent=𝒔𝒕 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

51. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

52. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

53. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝑶𝑨 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

54. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝑨 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

55. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝑨 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

56. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

57. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

58. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝟑.𝟕𝟖𝒘

59. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨 Tangent=𝟑.𝟕𝟖𝒘

60. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨 Tangent=𝟑.𝟕𝟖𝒘

61. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝑶𝑨 Tangent=𝟑.𝟕𝟖𝒘

62. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝒈𝑨 Tangent=𝟑.𝟕𝟖𝒘

63. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝒈𝑨 Tangent=𝟑.𝟕𝟖𝒘

64. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝒈𝟐𝟏.𝟔 Tangent=𝟑.𝟕𝟖𝒘

65. The Tangent Ratio Tangent=𝒔𝒕 Tangent=𝟒𝟗.𝟗𝟏𝟎𝟎 𝐓angent𝜃=OppositeAdjacent Tangent=𝒈𝟐𝟏.𝟔 Tangent=𝟑.𝟕𝟖𝒘

66. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

67. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

68. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

69. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

70. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

71. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA

72. The Tangent Ratio Remember: 𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ->TOA