Answers

Name
Class
14-4
Date
Practice
Form G
Area and the Law of Sines
Find the area of each triangle. Round your answers to the nearest tenth.
1.
2.
65ⴗ
14 in.
3.
11 in.
2 cm
35⬚
12 ft
32 ft
3 cm
10⬚
69.8 in.2
33.3 ft2
1.7 cm2
4. A triangle has sides of lengths 15 in. and 22 in., and the measure of the angle
between them is 958. Find the area of the triangle. 164.4 in.2
Use the Law of Sines. Find the measure x to the nearest tenth.
5.
12
x⬚
A
C
6.
14.9
10
18⬚
C
21
B
15.9
x
31⬚
43⬚
A
7. C
B
A
8.
13.1
23
123⬚
B
19
136.6
x
x⬚
54
21⬚
A
65⬚
C
B
9. In nGHJ , m/J 5 398, h 5 36 cm, and j 5 42 cm. Find m/H . 32.68
10. In nMNP, m/P 5 338, m 5 54 ft, and p 5 63 ft. Find m/M . 27.88
11. A hot-air balloon is observed from two points, A and B,
on the ground 800 ft apart as shown in the diagram. The angle of
elevation of the balloon is 65° from point A and 37° from point B.
Find the distance from point A to the balloon. 1025.5 ft
65⬚
A
37⬚
800 ft B
Find the remaining sides and angles of kPQR. Round your answers
to the nearest tenth.
12. m/Q 5 648, m/R 5 648, and r 5 8
13. m/Q 5 648, q 5 22, and r 5 14
mlP 5 528, p 5 7.0, q 5 8.0
mlP 5 81.18, mlR 5 34.98, p 5 24.2
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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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Name
14-4
Class
Date
Practice (continued)
Form G
Area and the Law of Sines
14. Two searchlights on the shore of a lake are located 3020 yd
apart as shown in the diagram. A ship in distress is
spotted from each searchlight. The beam from the first
searchlight makes an angle of 388 with the baseline.
The beam from the second light makes an angle of 578
with the baseline. Find the ship’s distance from each
searchlight. 2542.5 yd and 1866.4 yd
38⬚
57⬚
3020 yd
Find the area of kABC. Round your answer to the nearest tenth.
15. m/B 5 288, m/C 5 708, a 5 9.8
21.4 units2
16. m/A 5 428, a 5 4.17, c 5 5.02
10.4 units2
17. m/A 5 178, m/C 5 758, b 5 18.1
46.3 units2
18. m/C 5 818, b 5 6.7, c 5 9.3
25.1 units2
In kABC, mlA 5 258 and mlB 5 508. Find each value to the nearest tenth.
19. Find AC for BC 5 6.2 in.
11.2 in.
20. Find BC for AC 5 14.9 cm.
8.2 cm
21. Find AC for AB 5 53.7 ft.
42.6 ft
22. Find BC for AB 5 27.3 m.
11.9 m
23. An airplane is flying between two airports that are 35 mi
apart. The radar in one airport registers a 278 angle
between the horizontal and the airplane. The radar
system in the other airport registers a 698 angle
27⬚
between the horizontal and the airplane. How far is Airport 1
the airplane from each airport to the nearest tenth
of a mile? 32.9 mi from Airport 1, 16.0 mi from Airport 2
35 mi
69⬚
Airport 2
24. Writing Suppose you know the measures of two sides of a triangle and the
measure of the angle between the two sides. Can you use the Law of Sines to
find the remaining side and angle measures? Explain. No; answers may vary. Sample:
To use the Law of Sines you must know the measure of one angle and the measure of
the side opposite that angle, in addition to one other side or angle measure.
25. Reasoning How can you find the measures of the angles of nABC if you know
the measures of its sides and its area? Answers may vary. Sample: Use area 5 12 ab sin C
with two of its sides to ﬁnd mlC . Then use the Law of Sines to ﬁnd another angle
measure, and subtract the two known angle measures from 1808 to ﬁnd the third angle
measure.
Prentice Hall Gold Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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