Practice

Name
Class
Date
Practice
14-5
Form G
The Law of Cosines
Use the Law of Cosines. Find length x to the nearest tenth.
B
1.
B
2.
√2
x
x
8
45⬚
A
60⬚
A
C
10
5
x 5 !17 N 4.1
x 5 !84 N 9.2
Use the Law of Cosines. Find measure x to the nearest degree.
3.
4.
B
B
x8 5 538
√ 28
5
x⬚
A
x8 5 148
10
C
16
13
x⬚
A
12
C
5. In nXYZ, x 5 4 cm, y 5 7 cm, and z 5 10 cm. Find m/X. 18.28
6. In nFGH, f 5 32 in., g 5 79 in., and h 5 86 in. Find m/G. 66.78
7. In nABC, a 5 3 ft, b 5 2.9 ft, and c 5 4.6 ft. Find m/C. 102.48
8. In nFGH, f 5 34 m, g 5 18.9 m, and h 5 21.5 m. Find m/G. 30.48
9. In nABC, a 5 14 yd, b 5 16 yd, and c 5 18 yd. Find m/C. 73.48
Prentice Hall Gold Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
43
C
Name
Class
Date
Practice (continued)
14-5
Form G
The Law of Cosines
For Exercises 10−13, use the Law of Cosines and the Law of Sines. Find x to the
nearest tenth.
x8 5 151.98
10. Y
16⬚
4
9
x⬚
Z
X
x8 5 36.08
Y
11.
4.6
85⬚
x⬚
X
6.7
Z
12. In nABC, b 5 8 cm, c 5 7 cm, and m/A 5 1498. Find m/C. 14.48
13. In nFGH, f 5 7 yd, g 5 22 yd, and m/H 5 858. Find m/F. 18.18
14. The sides of a triangular lot are 158 ft, 173 ft, and 191 ft. Find the measure of
the angle opposite the longest side to the nearest tenth of a degree. 70.38
15. A car travels 50 mi due west from point A. At point B, the car turns and travels
at an angle of 358 north of due east. The car travels in this direction for 40 mi,
to point C. How far is point C from point A? 28.7 mi
16. a. In nABC, m/A 5 84.18, b 5 4.8, and c 5 7.2. Use the Law of Cosines to
find a and then use the Law of Sines to find the measure of angles B and C.
Round to the nearest tenth. a 5 8.2; mlB 5 35.48; mlC 5 60.58
b. Error Analysis Your classmate says that this triangle does not exist. You say
that it does. Who is correct? Explain. You; the angles of this triangle
add up to 1808, which is equal to the sum of the angles of any triangle.
Prentice Hall Gold Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
44

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