For more practice, see Extra Practice.
EXERCISES
A Practice by Example
Example 1
(page 287)
Example 2
(page 288)
Find each trigonometric ratio as a fraction in simplest
form. Exercises 1 and 2 have been started for you.
1. sin J = 18
■
2. cos J = 24
■
3. sin L
4. cos L
5.
368
L
6.
7.
t
t
428
6
438
87
In each figure, use the cosine ratio to find x to the nearest tenth.
8.
3.5
568
x
B Apply Your Skills
18
30
26
Example 4
(page 289)
K
In each figure, use the sine ratio to find t to the nearest tenth.
t
Example 3
(page 288)
24
J
9.
10.
52
x
358
308
x
16
11. Ladders A 16-ft ladder rests against a building and forms a 758 angle
with the ground. Draw a diagram to describe the problem. What is the
distance from the top of the ladder to the base of the building to the
nearest foot?
12. Trees A 40-m wire supports a tree. The wire is at an angle of 70 8 from
the ground. Draw a diagram to describe the problem. What is the
distance from the top of the wire to the base of the tree?
13. a. Open-Ended Find x by solving an equation
that involves the sine ratio.
b. Error Analysis A student reports that the
x
sin B is 7.4
. What error did the student make?
A
538
C
7.4
378
x
14. a. Water Parks A water slide starts at a height of
20 ft and descends in a straight line, making an angle of about
308 with the ground. Draw a diagram to describe the problem.
What is the length of the slide to the nearest foot?
b. A ladder allows you to reach the top of the slide. What is the
distance from the bottom of the ladder to the end of the slide?
5-9
The Sine and Cosine Ratios
B
289-291
Use the Pythagorean theorem to find n in Exercises 15–17. Then write
sin X and cos X as fractions in simplest form.
15. X
8
16.
6
17. Z
n
Z
n
Y
8
Z
X
n
Y
17
30
Y
15
X
18. Writing in Math Your friend is having trouble figuring out whether
to use the sine or the cosine ratio to solve a problem. Write an
explanation of how to choose an appropriate ratio.
B
19. a. In the figure at the right, sin B 艐 0.3333. Find the
approximate value of x to the nearest tenth.
b. What is the length of AB to the nearest tenth?
C Challenge
x
20. Stretch Your Thinking A certain three-digit number has a
square root that is a perfect square. The square root of its
square root is also a perfect square. What is the number?
A 12 C
Test Prep
Multiple Choice
S
x
298
618
9
R
T
Take It to the NET
Online lesson quiz at
www.PHSchool.com
Web Code: aca-0509
Short Response
289-291
Use kRST for Exercises 21 and 22.
21. Which equation can you use to find x?
x
A. cos 618 = 9x
B. sin 618 = 9
C. cos 298 = 9x
D. sin 298 = 9
x
22. What is x rounded to the nearest tenth?
F. 4.4
G. 7.9
H. 8.4
I. 10.3
23. In #XYZ, what is the sin Y in simplified
form?
5
A. 13
5
C. 12
B. 20
52
D. 12
13
24. a. Find a in the figure at the right using
the sin 218. Round to the nearest tenth.
b. Find b using the cos 218. Round to the
nearest tenth.
Chapter 5 Applications of Proportions
Z
91
35
X
84
A
b
218
17
Y
C
a
B
Mixed Review
Lesson 5-8
25. Algebra A wall 12 ft high casts a shadow 9 ft long. At the same time, a
nearby house casts a shadow 42 ft long. How tall is the house?
Lesson 5-7
26. You want to make a model of a gymnasium. The scale of the model
will be 1 in.i 5 12 ft. If the gymnasium is 77 ft high, what is the height
of your model?
Find the missing length. If necessary, round the answer to the nearest tenth.
Lesson 4-9
27.
28.
13 cm
8 cm
x
30 ft
14 ft
x
5-9
The Sine and Cosine Ratios
289-291