Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. A, c, and
a
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2.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. a, b, and
c
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3.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. C, c, and
A
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4.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. a, b,
and C
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5.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. b, B,
and c
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6.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. a, A,
and C
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7.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. B, a,
and c
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8.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. b, C,
and B
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9.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. a, c, and
C
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10.
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Determine whether there is
sufficient information for solving a triangle, with the given combination of angles and sides, by the
law of sines. b, A, and
B
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11.
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Solve the triangle. Round to
the nearest tenth when necessary or to the nearest minute as appropriate.
B = 53.2°
C = 100.6°
b
= 31.5
a. | A = 26.2°, a =
19.4, c = 40.7 | c. | A =
26.2°, a = 17.4, c = 38.7 | b. | A = 24.2°, a = 40.7, c =
19.4 | d. | A = 24.2°, a = 38.7, c =
17.4 |
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12.
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Solve the triangle. Round to
the nearest tenth when necessary or to the nearest minute as appropriate.
A = 28°20'
B =
24°10'
a = 38.1
a. | C = 128°30', b
= 63.7, c = 32.9 | c. | C = 127°30', b = 63.7, c =
32.9 | b. | C = 128°30', b = 32.9, c =
63.7 | d. | C = 127°30', b = 32.9, c =
63.7 |
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13.
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Solve the triangle. Round to
the nearest tenth when necessary or to the nearest minute as appropriate.
a. | C = 97°, a = 13.2 m, b
= 23.5 m | c. | C = 103°, a
= 23.9 m, b = 13.5 m | b. | C = 103°, a = 66.7 m, b = 37.6
m | d. | C = 103°, a = 13.5 m, b = 23.9
m |
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14.
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Solve the triangle. Round to
the nearest tenth when necessary or to the nearest minute as appropriate.
a. | B = 37.2°, b = 337.6 ft,
c = 273 ft | c. | B = 37.2°, b
= 273 ft, c = 337.6 ft | b. | B = 37.2°, b = 28.2 ft, c = 22.9
ft | d. | B = 36.8°, b = 270.5 ft, c = 337.6
ft |
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15.
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Find the area of triangle
ABC with the given parts. Round to the nearest tenth when necessary.
A = 39.7°
b = 11.8 in.
c =
6.3 in.
a. | 30.6
in.2 | c. | 28.6
in.2 | b. | 21.7 in.2 | d. | 23.7 in.2 |
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16.
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Find the area of triangle
ABC with the given parts. Round to the nearest tenth when necessary.
A = 39°40'
b = 16.5 m
c
= 10.5 m
a. | 27.7 m2 | c. | 112.6 m2 | b. | 110.6 m2 | d. | 55.3 m2 |
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17.
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Find the area of triangle
ABC with the given parts. Round to the nearest tenth when necessary.
b = 8.5 ft
A = 21°30'
C
= 101°40'
a. | 36 ft2 | c. | 15.5 ft2 | b. | 31 ft2 | d. | 10.5 ft2 |
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18.
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Two tracking stations are on
the equator 122 miles apart. A weather balloon is located on a bearing of N 32°E
from the western station and a bearing of N 12°E from the eastern station. How far, to the
nearest mile, is the balloon from the western station? Round to the nearest
mile.
a. | 349 mi | c. | 358 mi | b. | 239 mi | d. | 248 mi |
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19.
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To find the distance AB across
a river, a distance BC = 346 m is laid off on one side of the river. It is found that B
= 115.1° and C = 13.6°. Find AB rounded to the nearest
meter.
a. | 104 m | c. | 80 m | b. | 107 m | d. | 83 m |
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20.
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Lookout station B is
located 5 mi due east of station A. The bearing of a fire from A is S 12°10'W
and the bearing from B is S 30°50'W. Determine the distance from the fire to B (to the
nearest tenth of a mile).
a. | 17.3 mi | c. | 7.65 mi | b. | 15.3 mi | d. | 9.65 mi |
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21.
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A guy wire to a tower makes
a 67° angle with level ground. At a point 33 ft farther from the tower than the wire
but on the same side of the base as the wire, the angle of elevation to the top of the pole is
38°. Find the wire length (to the nearest foot).
a. | 84 ft | c. | 47 ft | b. | 89 ft | d. | 42 ft |
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22.
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Points A and B are on opposite
sides of a lake. Point C is 80.7 meters from A. The measure of angle BAC is
72°20', and the measure of angle ACB is determined to be 35°50'. Find
the distance between points A and B (to the nearest meter).
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23.
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An airplane is sighted at the
same time by two ground observers who are 2 miles apart and both directly west of the airplane.
They report the angles of elevation as 12° and  How high is the airplane?
Round to the nearest hundredth of a mile.
a. | 1.64 mi | c. | 0.72 mi | b. | 0.95 mi | d. | 0.42 mi |
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24.
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A rocket tracking station has
two telescopes A and B placed 1.7 miles apart. The telescopes lock onto a rocket and transmit
their angles of elevation to a computer after a rocket launch. What is the distance to the rocket
from telescope B at the moment when both tracking stations are directly east of the rocket telescope
A reports an angle of elevation of 22° and telescope B reports an angle of elevation
of 56°? Round to the nearest hundredth of a mile.
a. | 3.76 mi | c. | 0.77 mi | b. | 1.14 mi | d. | 2.52 mi |
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25.
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Find the area of a
triangular-shaped field with sides of 188.7 m and 197.5 m, and the included angle between
them measuring  Round to the nearest square
meter.
a. | 14,508
m2 | c. | 17,164
m2 | b. | 7254
m2 | d. | 34,328 m2 |
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26.
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A painter is going to apply a
special coating to a triangular metal plate on a new building. Two sides measure are 14.5 m and
5.1 m. She knows that the angle between these sides is 29.5°. What is the area
of the surface she plans to cover with the coating? Round to the nearest square
meter.
a. | 34 m2 | c. | 16 m2 | b. | 18 m2 | d. | 32 m2 |
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