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```Name
Date
Class
Practice B
LESSON
8-2
Trigonometric Ratios
Use the figure for Exercises 1–6. Write each trigonometric
ratio as a simplified fraction and as a decimal rounded to
the nearest hundredth.
1. sin A
2. cos B
!
#
3. tan B
7 ; 0.28
___
7 ; 0.28
___
25
4. sin B
"
24 ; 3.43
___
7
25
5. cos A
6. tan A
24 ; 0.96
___
24 ; 0.96
___
25
7 ; 0.29
___
25
24
Use special right triangles to write each trigonometric ratio as a
simplified fraction.
1
__
7. sin 30
8. cos 30
2
3
___
3
10. tan 30
11. cos 45
3
___
2
2
___
2
9. tan 45
1
12. tan 60
3
Use a calculator to find each trigonometric ratio. Round to the
nearest hundredth.
0.90
13. sin 64°
14. cos 58°
0.53
15. tan 15°
0.27
Find each length. Round to the nearest hundredth.
9
16.
(
17.
18.
'
+
0.8 mi
12.2 in.
8
55°
41°
XZ
14.03 in.
19.
36°
3
100 cm
)
:
4
HI
57.36 cm
72°
8.68 km
#
%
2 ft
&
51°
\$
2
ST
31 yd
21.
,
0.36 mi
KM
\$
20.
%
5.1 km
27°
-
EF
95.41 yd
12
DE
3.18 ft
Holt Geometry
Name
Date
Class
Name
Practice A
LESSON
8-2
8-2
In Exercises 1–3, fill in the blanks to complete each
definition. Then use side lengths from the figure to
complete the indicated trigonometric ratios.
�
�
�
�
Trigonometric Ratios
Use the figure for Exercises 1–6. Write each trigonometric
ratio as a simplified fraction and as a decimal rounded to
the nearest hundredth.
�
�
opposite
1. The sine (sin) of an angle is the ratio of the length of the leg
hypotenuse
.
the angle to the length of the
1. sin A
c
b
b
a
5. cos L
�
_3_ ; 0.60
10
�
6. tan M
_4_ ; 0.80
8. cos 30�
2
�
�3
___
3
10. tan 30�
6
11. cos 45�
�3
___
2
�
�2
___
2
9. tan 45�
1
12. tan 60�
�3
�
�
8
Use a calculator to find each trigonometric ratio. Round to the
nearest hundredth.
_4_ ; 1.33
5
5
24
�
_1_
7. sin 30�
Use the figure for Exercises 4–6. Write each trigonometric
ratio as a simplified fraction and as a decimal rounded to
the nearest hundredth.
7 ; 0.29
___
25
Use special right triangles to write each trigonometric ratio as a
simplified fraction.
b
tan B � ___
a
tan A � ___
24 ; 0.96
___
25
opposite
3. The tangent (tan) of an angle is the ratio of the length of the leg
the angle to the length of the leg
to the angle.
7
6. tan A
24 ; 0.96
___
c
24 ; 3.43
___
5. cos A
a
cos B � ___
cos A � ___
c
3. tan B
25
4. sin B
�
�
��
7 ; 0.28
___
25
2. The cosine (cos) of an angle is the ratio of the length of the leg
hypotenuse
to the angle to the length of the
.
�
��
�
2. cos B
7 ; 0.28
___
b
sin B � ___
a
sin A � ___
c
Class
Practice B
LESSON
Trigonometric Ratios
4. sin L
Date
3
0.90
13. sin 64°
14. cos 58°
0.53
0.27
15. tan 15°
Use a calculator to find each trigonometric ratio. Round to the nearest hundredth.
8. cos 47�
7. sin 33�
9. tan 81�
Find each length. Round to the nearest hundredth.
6.31
0.68
0.54
16.
�
62°
�
�
�
12.46 m
12.
�
5 ft
�
�
27°
13. The glide slope is the path a plane uses while it is landing on
a runway. The glide slope usually makes a 3� angle with the
ground. A plane is on the glide slope and is 1 mile (5280 feet)
from touchdown. Use the tangent ratio and a calculator to
find EF, the plane’s altitude, to the nearest foot.
11
Name
8-2
�
�
����
Date
Class
Holt Geometry
4.
9 ft
78°
�
�
�
x � ___
1
� ____
�
�
x� 2
�2
�
2
�
___
�
2
13
�
�
�
�
60°
45°
� ��
2
2�
�
45°
�
�
�
30°
�
� ��
3
�
�
�2 .
So sin 45� � ___
2
Write each trigonometric ratio as a fraction and as a decimal
rounded to the nearest hundredth.
1. sin K
�
2. cos H
15 � 0.88
___
�
17
8
�
15
�
15 � 0.88
___
17
17
3. cos K
4. tan H
8 � 0.47
___
8 � 0.53
___
17
15
Use a special right triangle to write each trigonometric ratio as a fraction.
6. tan 45�
5. cos 45�
�
�2
___
_1_ � 1
1
2
7. sin 60�
44.1 ft
8. tan 30�
�
�
�3
___
15 km
15.18 km
�
leg opposite �Q
sin 45� � sin Q � ______________
hypotenuse
75°
�3
___
2
6.9 cm
6.78 cm
�
�
You can use special right triangles to write trigonometric ratios as fractions.
Use the formula you developed in Exercise 5 to find the missing side length in
each triangle. Round to the nearest hundredth.
leg opposite �A
�
leg opposite �A
tan A � ________________ � _4_ � 1.33
3
7 in.
44.1 ft
�
hypotenuse
cos A � ________________ � _3_ � 0.6
5
hypotenuse
2
2
2
2
2
2
2
gives b � 2bx � x � y � a . Substituting, b � 2bx � c � a .
x
_
_
But cos A � c, so x � c cos A. Another substitution gives
2
2
2
a � b � c � 2bc cos A.
4 km 85°
Holt Geometry
Trigonometric Ratios
2
2
2
It also shows that (b � x) � y � a . Expanding the latter equation
55°
Class
Trigonometric Ratios
12.05 in
8.
Date
Reteach
leg opposite �A
sin A � ______________ � _4_ � 0.8
5
hypotenuse
Possible answer: The Pythagorean Theorem shows that x 2 � y 2 � c 2.
7.
3.18 ft
DE
�
�
2
28.39 ft
7.7 cm
�
51°
95.41 yd
12
�
�
5. The law of cosines is a formula to find the length of the third side of
any triangle given the lengths of two sides and the measure of the
�
�
�
included angle. (Note: The law of cosines applies to any triangle,
but deriving it for an obtuse triangle requires more knowledge than
�
�����
�
you have learned so far.) In the figure, suppose the lengths b and c
�
and the measure of �A are known. Develop the law of cosines to find a.
Explain your answer. (Hint: Use the cosine function and the Pythagorean Theorem.)
6.
EF
Name
7.1 in.
2
18.66 m
�
2 ft
�
8.68 km
73°
7.6 m
2
31 yd
�
Use the formula you developed in Exercise 1 to find the area of each triangle.
Round to the nearest hundredth.
43°
21.
�
72°
�
0.36 mi
KM
�
ST
8-2
11 ft
20.
�
27°
277 feet
Possible answer: Draw an altitude from �B and call its length h. Then
_
sin A � _h
c , so h � c sin A. The formula for the area of a triangle is
Area � _1_ base � height. Substitution gives Area � _1_ bc sin A.
2
2
35°
57.36 cm
�
LESSON
3.
HI
5.1 km
Trigonometric Ratios
7.2 m
36°
�
1. Given the lengths of two sides of a triangle and the measure of the
included angle, the area of the triangle can be found. In the figure,
suppose the lengths b and c and the measure of �A are known. Develop
a formula for finding the area. Explain your answer. (Hint: Draw an altitude.)
2.
0.8 mi
�
��
Practice C
LESSON
14.03 in.
�
2.55 feet
RS
�
100 cm
�
�
19.
�
�
19.70 mm
QP
�
55°
41°
XZ
38°
25 mm
11 m
BD
�
11.
18.
�
12.2 in.
Use a calculator and trigonometric ratios to find each length. Round to the
nearest hundredth.
10.
17.
�
3
22.83 ft
Holt Geometry