Geometry' Support Unit 4—Right Triangles Trig Notes

Name Date

TRIG RATIOS IN RIGHT TRIANGLES NOTES #1

REMEMBERING PYTHAGOREAN THEOREM

102 2 2

h enusv

2 2

otcn so

IDENTIFY THE RATIOSz

l. Identify the side that is opposite ZZ.

2. Identify the side that is adjacent to ZZ. Z

3. Identify the hypotenuse.

H

14. Identify the side that is opposite ZH.

5. Identify the side that is adjacent to ZH.

6. Identify the hypotenuse.

In a right triangle, there are several ratios that can be created using trigonometry. There arethree main trig ratios and thenthe reciprocals of those ratios.

3

Ratio Definition

orPSine =

adCosine =

OPPTangent =

Exam le

sin a =

cos a —

4

33

3

3

Exam le3

sin B =

cos =5

3tan a =

Relationshi Between Ratios

sin a =

cos a =

tan a =

Geometry Support Unit 4—Right Triangles Trig Notes

Remembering Trigonometric Ratios: 'OH OAH TOAOld

of 0 =opposite

hypotenuse

adjacentHypo enuse

of e hypotenuseOpposite

8f=O =opposite

adjacent

sine.

opponft

HyptcnUs1J

Adjacent

Examples:

h500 ft

335 ft

0 31)

cos : 33bh 500

Tan 480.0-%

361 fth

500 ft 400 ft

530

Oft

Sin 530—— :5

cos 530B 3

0 4Tan 53 0

5

35

T ang€nf

o pposif6

Adjacent

h500 ft

600

Oft

Sin 60 0

500

250cos 60 0

500

433Tan 60 0

433 ft

3250

Geometry Support Unit 4--Right Triangles Trig Notes

Find the value of each trigonometric ratio. Express your answer as a frqgtion in lowest terms.

O SINCE 2. SINC=

2921

20 (L B

3. cos c =

3915

36

9. TAN A =

30

4. cos c =

10. TAN x =

3712

40 a. B

10

or vnolboff

17 15

4536

11 3

fDGmpIi

Geometry Support Unit 4—Right Triangles Trig Notes

In the following problems, DRAW stick-man standing where the angle is and MARK each

given side as A (adjacent), O (opposite), or H (hypotenuse). Then TELL which TRIG RATIOyou have. You NOT be solving the problem for x (we haven't learned how YET).

l. Which trig ratio is represented?

hB. COSCOS 69

x390

2. Which trig ratio is represented?

A. SINhB. COS

xC TAN

3. Which trig ratio is represented?

A. SIN180B. COS

52 0

4. Which trig ratio is represented?

A. SIN620

B. COS Sin :C. TAN

52 0

Geometry Support Unit 4—Right Triangles Trig

Draw AABC where ZABC = 900 AB = BC = 15, and AC = 17.,

1. What is tan C? usg15

2. WhatissinA? 15

AABC where LACB = 900, AC = 5, and CB = 12.

3. What is the length of AB? 26tlADl CLlbl

4. What is cosA? 5

n 135. Whatistan B? L 5

ACAT where LATC = 900, CA = 53, and CT = 28.

6. What is the length of AT?1015 --cL

7- What issinC? : 45n 33

8. What is tan 7-99-5

12AABC where LB = 900 and sin A = — •

20

9. What is the length of AB?L6bcDæ

is tan —

11.WhatiscosA?0.- _ 1b _ 4¯ 20

AHAT where ZH = 900 and tan T = —35

12. What is the length of AT?I bbq

5

46

1b

IL

Notes

13

12-

53

10

31

3613. What is sin A?

14.What is cos T?

PracticeUnit 4: Right Triangle Trig

Geometry SupportDate

Name

Day 1 Practice—Trig Ratios

find each ratio and be sure to reduce, if possible.

32 0 2. 1. Tanz x

tant' 3 24

z 1n simplify

3. Cos A 4.

41 h

09 40B 40

Draw AABC where ZABC = 900, AB = 6, BC = 8, and AC = 10.

5. WhatistanC? 46. What is sin A?

Draw AABC where ZACB 900, AC = 7, and CB = 24.

7. What is the length of AB?

8. What iscosA?25

9. What is tan B? :

Draw ACAT where ZATC = 900, CA = 41 , and CT = 9.

10. What is the length of AT?

ll. What is sin C? Sin (JAL

n 4112. What is tan A? 40

20 0Sin X z

h 2515

5

5 PJi(YlflIfy

Sin C

21

463 h

345

36

27

tosirnqlify

10

45

25 : c

T IS

C'

boo

Geometry Support Unit 4: Right Triangle Trig Practice

10Draw AABC where LB = 900 and sinA =

26

13. What is the length of AB?

10 514. What is tan A?

15. WhatiscosA?E- -M. —

8Draw AHAT where LH = 900 and tanT = —

15

16. What is the length of AT? I

17. What is sin — — 15

h 1118. WhatiscosT? 15

n Il

2bL

b L

: 57b

b: 24

10

16) f

16

In the following problems, using the angle that is given, MARK each given side as A (adjacent), O(opposite), or H (hypotenuse). Then TELL which TRIG RATIO you have. You will NOT be solving theproblem for x (we haven't learned how YET).

19. Whic ratio is represented?

A. SINs

C. TAN

O

Sin:

m. Which trig ratio is represented?

D. SINos

F. TAN

21. Which trig ratio is represented?

G.

l. AN cos-h

9 ll h

x90

20

13

h 90.-