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Name
Class
Date
Practice
14-5
Form K
The Law of Cosines
Use the Law of Cosines. Find length x to the nearest tenth.
B
1.
x
To start, list the known information.
a 5 10, b 5 20, m/C 5 408
Use the form of the Law of Cosines that has c2 on
one side:
10
40⬚
A
c2 5
20
2
a 1
C
b2 2 2ab cos C
z
2
z
z
z
2
z
z z
z
10
20
10
20
5 a b 1 a b 2 2a b a b cos 408
z
z
193.58
< z
z z
z
13.9
c < $ 193.58 < B
2.
20.0
22
B
3.
85⬚
12
x
31.3
30
A
A
50⬚
C
25
C
x
Use the Law of Cosines. Find measure x to the nearest tenth of a degree.
B
4.
To start, list the known information.
x⬚
14
16
Use the form of the Law of Cosines that contains /B:
b2 5 a2 1 c2 2 2ac cos B
C
10
A
a 5 14, b 5 10, c 5 16
2
2
2
10
14
16
14
16
z z 5 a z zb 1 a z zb 2 2a z zb a z zb cos B
196
256
448
100
z z 5 z z 1 z z 2 z z cos B
2352 z 5 z 2448 z cos B
z z
352
z
cos B 5 448
z
z z
352
z
38.28
m/B 5 cos21 a b < 448
B
5.
A
15
6
x⬚
18
B
6.
51.3°
x⬚
15
C
A
20
Prentice Hall Foundations Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
45
117.5°
8
C
1/--pages
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