chapter 7 trigonometric applications to triangles · exercise set 7.3: the law of sines and the law...

CHAPTER 7 Trigonometric Applications to Triangles

University of Houston Department of Mathematics 614

Section 7.3: The Law of Sines and the Law of Cosines

Solving Oblique Triangles

Solving Oblique Triangles

SECTION 7.3 The Law of Sines and the Law of Cosines

MATH 1330 Precalculus 615

The Law of Cosines:



(SSS)

Example:

Solution:



(SAS)

Example:

Solution:

The Law of Sines:



(SAA)

Example:

Solution:



(SSA)



Example:



Solution:

Example:

Solution:



Example:

Solution:

Example:

Solution:



Additional Example 1:

Solution:




Solution:

Exercise Set 7.3: The Law of Sines and the Law of Cosines


Find the indicated part of each triangle. Give exact

values whenever possible. Otherwise, round answers

to the nearest hundredth. If no such triangle exists,

state “No such triangle exists.”

1. ABC

9 ma

5 mc

71B

?b

2. ABC

16 cma

35A

65B

?b

3. ABC

9 ina

60A

45C

?c

4. RST

8 mms

135S

30T

?t

5. NAP

5 inn

10 ina

7 inp

?N

6. KLM

3 ink

4 inl

8 inm

?M

7. SUN

10 cmn

63N

48S

?s

8. PSU

2.5 ins

112P

37U

?p

9. CAN

11cmc

9 cma

14 cmn

?C

10. HAT 14 mma

45A

15T

?h

11. RST

9 mmr

15 ins

4 int

?R

12. BOX

10 cmo

7 cmx

43B

?b

13. TRY 12 cmy

30T

105R

?t



8 cm4 cm

A T

C

50o

14. WIN

4.9 ftw

42I

100N

?n

Find all possible measures for the indicated angle of

the triangle. (There may be 0, 1, or 2 triangles with the

given measures.) Round answers to the nearest

hundredth. If no such triangle exists, state “No such

triangle exists.”

15. DEF

25 mmd

13 mme

21E ?D

16. CAR

3 cmc

7 cmr

15C

?R

17. ABC

9 cmb

6 cmc

95B

?C

18. BUS

18 mmb

16 mmu

120B

?U

19. GEO

11cmg

4 cmo

33O

?G

20. ABC

10 ftb

7 ftc

70B

?A

21. ANT

12 cmn

15 cmt

129T

?A

22. JAY

15 inj

9 iny

160Y

?J

Solve each of the following triangles, i.e. find all

missing side and angle measures. There may be two

groups of answers for some exercises. Round answers

to the nearest hundredth. If no such triangle exists,

state “No such triangle exists.”

Note: Figures may not be drawn to scale.

23.

24.

25. WHY

8 inh

4 iny

28Y

9.42 ft

F

ED

35o

125o



128o

30 cm

17 cm

25 cm

T

R

U

S

23 cm

18 cm

8 cm

G U

C

O

49o

12 in

17 in

15 in

Q

D A

U

122o

115o

26. ABC

12 ina

17 inb

6 inc

27. RUN

7 cmr

12 cmu

4 cmn

28. JKL

6 mj

5 mk

74J

29. PEZ 12 mmp

10 mmz

130E

30. BAD

11 ftb

9 fta

5 ftd

31. PIG

6 cmp

13 cmi

11cmg

32. QIZ

12.4 mmi

11.5 mmz

66Z

33. DEF

10 mmd

3 mmf

21F

34. SEA

8 cms

9 cme

21cma

Find the area of each of the following quadrilaterals.

Round all intermediate computations to the nearest

hundredth, and then round the area of the

quadrilateral to the nearest tenth.


35.

36.

37.

38.

123o

19 in

33 in

14 in

20 inA

KE

C



Answer the following. Round answers to the nearest

hundredth.


39. (a) Use the Law of Sines or the Law of Cosines

to find the measures of the acute angles of a

3-4-5 right triangle.

(b) Use right triangle trigonometry to find the

measures of the acute angles of a 3-4-5 right

triangle.

40. (a) Use the Law of Sines or the Law of Cosines

to find the measures of the acute angles of a

7-24-25 right triangle.

(b) Use right triangle trigonometry to find the

measures of the acute angles of a 7-24-25

right triangle.

41. In HEY , 125H and 5

4h y . Find the

measures of E and Y .

42. In FUN , 100F and 2

3u f . Find the

measures of U and N .

43. Find the length of AD .

44. Find the length of AD .

7 mm 11 mm

8 mm6 mmB

A

CD

14 mm 6 mm

5 mm 8 mm C

A

B D

chapter 7 trigonometric applications to triangles · exercise set 7.3: the law of sines and the law...

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