Trig SOH CAH TOA A C B

WHICH HOUSE WOULD YOU RATHER LIVE IN? House number 1 OR House number 2?

House number 1

House number 2

Trigonometry Trig means angle measurement Trig deals with the relation between sides and angles Trig helps you find the length of a side or the measure of an angle

What might you use trig for? To build a house correctly Is your ladder long enough to reach the gutters? What is the shortest distance between two points? What is the height and width of a TV screen? Where will your furniture fit in a room? What is the height of a building or a tree? How can you build a staircase?

Trigonometric Ratios Sine Sin = _opposite_ hypotenuse Cosine Cos = _adjacent_ Tangent Tan = opposite adjacent

Trig Memory Clue SOH CAH TOA S ine C osine T angent O pposite A djacent O pposite H ypotenuse H ypotenuse A djacent

SIN, COS, and TAN Find sine, cosine, and tangent of acute angles only. 5 2 Sin = Cos = C B Tan = 3

B 11 T L 3 6.7 F 14 17.8 6 Sin Cos Tan R Sin Cos Tan G

…for the red acute angle only. 6 7 12 A Y 13.4 9 R Sin Cos Tan Sin Cos Tan 11.4 X U Sin Cos Tan 14.2 9 E Z 11

PRACTICE SIN, COS, and TAN 1. 2. 3. A N A 10 25 8 12 13 24 H S B C T L 6 5 7 Sin Cos Tan Sin Cos Tan Sin Cos Tan …for both acute angles.

R 3 H A 7.1 6.2 3 Sin Cos Tan A Sin Cos Tan M M B I A M 3.5 Sin Cos Tan R Sin Cos Tan B A M R B R B

W 4. 5. D Sin Cos Tan 16 12 15 Sin Cos Tan 20 Y J P 9 V 12 6. 9 16 N C Sin Cos Tan 13 L

7. P 8. 3 25 Y T E 5 Sin Cos Tan 7 4 24 Sin Cos Tan I A Q 9. 24 10 Sin Cos Tan G D 26

C 10. 11. F 6 10 Sin Cos Tan O 8 26 S Sin Cos Tan 24 12. G 15 Z I 10 E 25 20 Sin Cos Tan T

K 13. 14. M 1 Sin Cos Tan S 1 2 B Sin Cos Tan W 1 I 15. F 4 2 Sin Cos Tan C H

16. 6.2 17. F E L 6.2 Sin Cos Tan 3.5 B 7.1 Sin Cos Tan 7.8 10 O 18. M 6.4 Sin Cos Tan T 4.7 D 4.3 U

19. Q 20. E Sin Cos Tan 4.1 7.8 7 T 6 G 5.6 Z 5 A 21. 30 B Sin Cos Tan D 34 Sin Cos Tan 16 C

22. 23. R Sin Cos Tan 32 I J 24 40 25 24 Sin Cos Tan A 32 B O C 24. 48 Sin Cos Tan 14 G 50 L

What is the hypotenuse? It is always across from the right angle. It is always the longest side. hypotenuse

Hypotenuse A L A E G E C A L A G B

Practice marking the hypotenuse 1. 2. C B I E 3. 4. J K D L F

Practice marking the hypotenuse 6. 5. B C A C 8. 7. B B C A B

Practice marking the hypotenuse B 10. 9. A C A C 12. C 11. B B B A C

What is the opposite side? It is the side across from the angle you’re working with. A The side opposite is The side opposite is C B

Opposite Side O I I K N P K M N P J S D D M V V S D M Side opposite   K Side opposite N Side opposite P K M N P J S D D M V V Side opposite   Side opposite S D M

Practice marking opposite side 1. 2. C T D A C B 3. 4. D O G B

Practice marking opposite side 5. 6. Y D D C L R I 7. 8. O G P W

Practice marking the opposite side U 10. 9. F M D G A 12. 11. Z I A G Z

What is the adjacent side? The adjacent side runs alongside the angle (but it won’t be the hypotenuse). The side adjacent to is B The side adjacent to is C A

Practice marking the adjacent side B M 1. 2. O Side adjacent to <A <B Side adjacent to <P <O C A B C R 3. 4. P <A Side adjacent to A G <R <A Side adjacent to A <B

Practice marking the adjacent side F N E 5. 6. D U D I R P A 7. 8. L B

Practice marking the adjacent side O U 9. 10. S F G W N 11. 12. G D A G U

STRAW ACTIVITY You will be given 3 straws and a piece of poster board. Place the straws on the poster board in the shape of a right triangle Label the angles with your initials Label the hypotenuse I will come around and give you one of the angles: You will label the opposite side and the adjacent side

STRAW ACTIVITY EXAMPLE Using angle L, label the opposite and adjacent sides L hypotenuse adjacent A T opposite

Practice marking different sides 1. 2. D E H I 3. S Y 4. E V O R

5. M P P C 6. A A 7. P P 8. A N T A

O T 9. O 10. Y N U 11. S 12. K M J A V

A 13. 14. M J C D A E 15. N E 16. O W L

Q Y 17. 18. R T W E 19. A G 20. F S D H

J 21. 22. K L O M N C B 23. 24. P V X I