1. Right Triangle Trigonometry

2. Let’s Say We Have This Right Triangle10 H
1.74 O
10° Ɵ A
The reference angle is equal to 10°
The hypotenuse is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟏.𝟕𝟒 𝟏𝟎 = 0.174
The opposite is equal to 1.74

3. Calculator
Get it out of your bag

4. Calculator
Zoom In
Hit the ‘sin’ button
Type in ’10’
Hit ‘enter’

5. Calculator
sin (10) =

6. Let’s Say We Have This Right Triangle10 H
3.42 O
20° Ɵ A
The reference angle is equal to 20°
The hypotenuse is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟑.𝟒𝟐 𝟏𝟎 = 0.342
The opposite is equal to 3.42

7. Calculator
Zoom In
Hit the ‘sin’ button
Type in ’20’
Hit ‘enter’

8. Calculator
sin (20) =

9. Let’s Say We Have This Right Triangle10 H O 5
30° Ɵ A
The reference angle is equal to 30°
The hypotenuse is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟓 𝟏𝟎 = 0.5
The opposite is equal to 5

10. Calculator
Zoom In
Hit the ‘sin’ button
Type in ’30’
Hit ‘enter’

11. Calculator
sin (30) = 0.5

12. sin Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞
What does this mean?
The ratio of the opposite side length divided by the hypotenuse side length is equal to the sin of the reference angle.
sin Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 H O
sin Ɵ = 𝐎 𝐇 Ɵ A

13. Let’s Say We Have This Right Triangle10 H O
10° Ɵ
9.85 A
The reference angle is equal to 10°
The hypotenuse is equal to 10
The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟗.𝟖𝟓 𝟏𝟎 = 0.985
The adjacent is equal to 9.85

14. Calculator
Zoom In
Hit the ‘cos’ button
Type in ’10’
Hit ‘enter’

15. Calculator
cos (10) =

16. Let’s Say We Have This Right Triangle10 H O
20° Ɵ
9.40 A
The reference angle is equal to 20°
The hypotenuse is equal to 10
The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟗.𝟒𝟎 𝟏𝟎 = 0.940
The adjacent is equal to 9.40

17. Calculator
Zoom In
Hit the ‘cos’ button
Type in ’20’
Hit ‘enter’

18. Calculator
cos (20) =

19. Let’s Say We Have This Right Triangle10 O
30° Ɵ
8.66 A
The reference angle is equal to 30°
The hypotenuse is equal to 10
The ratio of the 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟖.𝟔𝟔 𝟏𝟎 = 0.866
The adjacent is equal to 8.66

20. Calculator
Zoom In
Hit the ‘cos’ button
Type in ’30’
Hit ‘enter’

21. Calculator
cos (30) =

22. cos Ɵ = 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞
What does this mean?
The ratio of the adjacent side length divided by the hypotenuse side length is equal to the cos of the reference angle.
cos Ɵ = 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 𝐇𝐲𝐩𝐨𝐭𝐞𝐧𝐮𝐬𝐞 H O
cos Ɵ = 𝐀 𝐇 Ɵ A

23. Let’s Say We Have This Right Triangle
1.76 O
10° Ɵ 10 A
The reference angle is equal to 10°
The adjacent is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟏.𝟕𝟔 𝟏𝟎 = 0.176
The opposite is equal to 1.76

24. Calculator
Zoom In
Hit the ‘tan’ button
Type in ’10’
Hit ‘enter’

25. Calculator
tan (10) =

26. Let’s Say We Have This Right TriangleO
3.64
20° Ɵ A 10
The reference angle is equal to 20°
The adjacent is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟑.𝟔𝟒 𝟏𝟎 = 0.364
The opposite is equal to 3.64

27. Calculator
Zoom In
Hit the ‘tan’ button
Type in ’20’
Hit ‘enter’

28. Calculator
tan (20) =

29. Let’s Say We Have This Right TriangleO
5.77
30° Ɵ A 10
The reference angle is equal to 30°
The adjacent is equal to 10
The ratio of the 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒔𝒊𝒅𝒆 = 𝟓.𝟕𝟕 𝟏𝟎 = 0.577
The opposite is equal to 5.77

30. Calculator
Zoom In
Hit the ‘tan’ button
Type in ’30’
Hit ‘enter’

31. Calculator
tan (30) =

32. tan Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭
What does this mean?
The ratio of the opposite side length divided by the adjacent side length is equal to the tan of the reference angle.
tan Ɵ = 𝐎𝐩𝐩𝐨𝐬𝐢𝐭𝐞 𝐀𝐝𝐣𝐚𝐜𝐞𝐧𝐭 H O
tan Ɵ = 𝐎 𝐀 Ɵ A

33. Trigonometric Functions
sin Ɵ = 𝐎 𝐇
cos Ɵ = 𝐀 𝐇
tan Ɵ = 𝐎 𝐀
SOH
CAH
TOA H O Ɵ A